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JEE Physics

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Chapter 11

Electrostatics - all with Video Answers

Educators

Chapter Questions

02:01

Problem 1520

When a Piece of Polythene is rubbed with wool, a charge of $-2 \times 10^{-7}$ is developed on polythene. The mass transferred to polythene is $\ldots \mathrm{kg}$.
(A) $11.38 \times 10^{-19}$
(B) $5.69 \times 10^{-19}$
(C) $2.25 \times 10^{-19}$
(D) $9.63 \times 10^{-19}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:07

Problem 1521

The protonic charge in $100 \mathrm{gm}$ of water is $\ldots \ldots . . \mathrm{c}$
(A) $4.8 \times 10^{5}$
(B) $5.4 \times 10^{6}$
(C) $3.6 \times 10^{4}$
(D) $4.9 \times 10^{6}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:53

Problem 1522

A copper sphere of mass $2 \mathrm{gm}$ contains about $2 \times 10^{22}$ atoms. The charge on the nucleus of each atom is 29e. what fraction of electrons removed from the sphere to give it a charge of $2 \mu \mathrm{c}$ ?
(A) $2 \times 10^{-10}$
(B) $1.19 \times 10^{-12}$
(C) $1.25 \times 10^{-11}$
(D) $2.16 \times 10^{-11}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:51

Problem 1523

The rate of alpha particle falls on neutral sphere is $10^{12}$ per second. The time in which sphere gets charged by $2 \mu \mathrm{c}$ is ru. $\mathrm{sec}$
(A) $2.25$
(B) $3.15$
(C) $6.25$
(D) $1.66$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:57

Problem 1524

A charge $\mathrm{Q}$ is divided into two parts and then they are placed at a fixed distance. The force between the two charges is always maximum when the charges are $\ldots \ldots$
(A) $(Q / 3),(Q / 3)$
(B) $(\mathrm{Q} / 2),(\mathrm{Q} / 2)$
(C) $(Q / 4),(3 Q / 4)$
(D) $(Q / 5),(4 Q / 5)$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:41

Problem 1525

Two point charges repel each other with a force of $100 \mathrm{~N}$. One of the charges is increased by $10 \%$ and other is reduced by $10 \%$. The new force of repulsion at the same distance would be $\ldots \ldots \mathrm{N}$.
(A) 121
(B) 100
(C) 99
(D) 89

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:40

Problem 1526

Given that $q_{1}+q_{2}=q$ if the between $q_{1}$ and $q_{2}$ is maximum, $\left(\mathrm{q}_{1} / \mathrm{q}\right) \ldots \ldots \ldots$
(A) 1
(B) $0.75$
(C) $0.25$
(D) $0.5$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:12

Problem 1527

Two small conducting sphere of equal radius have charges $+1 \mathrm{c}$ and $-2 \mathrm{c}$ respectively and placed at a distance $\mathrm{d}$ from each other experience force $F_{1}$. If they are brought in contact and separated to the same distance, they experience force $F_{2}$. The ratio of $F_{1}$ to $F_{2}$ is $\ldots \ldots \ldots \ldots$
(A) $-8: 1$
(B) $1: 2$
(C) $1: 8$
(D) $-2: 1$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:27

Problem 1528

Three charges, each of value $Q$, are placed at the vertex of an equilateral triangle. A fourth charge $q$ is placed at the centre of the triangle. If the charges remains stationery then, $q=\ldots \ldots \ldots$
(A) $(\mathrm{Q} / \sqrt{2})$
(B) $-(\mathrm{Q} / \sqrt{3})$
(C) $-(Q / \sqrt{2})$
(D) $(\mathrm{Q} / \sqrt{3})$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:50

Problem 1529

Iwo small charged spheres repel each other with a force $2 \times 10^{-3} \mathrm{~N}$. The charge on one sphere is twice that of the other. When these two spheres displaced $10 \mathrm{~cm}$ further apart the force is $5 \times 10^{-4} \mathrm{~N}$, then the charges on both the spheres are.......
(A) $1.6 \times 10^{-9} \mathrm{C}, 3.2 \times 10^{-9} \mathrm{C}$
(B) $3.4 \times 10^{-9} \mathrm{C}, 11.56 \times 10^{-9} \mathrm{C}$
(C) $33.33 \times 10^{9} \mathrm{C}, 66.66 \times 10^{-9} \mathrm{C}$
(D) $2.1 \times 10^{-9} \mathrm{C}, 4.41 \times 10^{-9} \mathrm{C}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:02

Problem 1530

Three charges $-q_{1}+q_{2}$ and $-q_{3}$ are placed as shown in figure. The $\mathrm{x}$ component of the force on $-\mathrm{q}_{1}$ is proportional to $\ldots \ldots$
(A) $\left(q_{2} / b^{2}\right)-\left(q_{3} / a^{2}\right) \sin \theta$
(B) $\left(q_{2} / b^{2}\right)-\left(q_{3} / a^{2}\right) \cos \theta$
(C) $\left(\mathrm{q}_{2} / \mathrm{b}^{2}\right)+\left(\mathrm{q}_{3} / \mathrm{a}^{2}\right) \sin \theta$
(D) $\left(q_{2} / b^{2}\right)+\left(q_{3} / a^{2}\right) \cos \theta$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:09

Problem 1531

1wo equal negative charges $-q$ are fixed at points $(0, a)$ and $(0,-a)$. A positive charge $Q$ is released from rest at the point $(2 \mathrm{a}, \mathrm{o})$ on the $\mathrm{X}-$ axis. The charge $\mathrm{Q}$ will $\ldots \ldots$
(A) move to the origin and remain at rest there
(B) execute simple harmonic motion about the origin
(C) move to infinity
(D) execute oscillations but not simple harmonic motion

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:58

Problem 1532

Four charges, each equal to $-\mathrm{Q}$, are placed at the corners of a square and a charge $+q$ is placed at its centre. If the system is in equilibrium, the value of $\mathrm{q}$ is
(A) $(Q / 4)(1+2 \sqrt{2})$
(B) $-(\mathrm{Q} / 4)(1+2 \sqrt{2})$
(C) $-(Q / 2)(1+2 \sqrt{2})$
(D) $(Q / 2)(1+2 \sqrt{2})$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:43

Problem 1533

For the system shown in figure, if the resultant force on q is zero, then $q=\ldots \ldots \ldots$
(A) $-2 \sqrt{2} \mathrm{Q}$
(B) $2 \sqrt{2} \mathrm{Q}$
(C) $2 \sqrt{3} \mathrm{Q}$
(D) $-3 \sqrt{2} Q$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:11

Problem 1534

Two point positive charges $q$ each are placed at $(-a, 0)$ and $(a, 0)$. A third positive charge $q_{0}$ is placed at $(0, y)$. For which value of $\mathrm{y}$ the force at $q_{0}$ is maximum $\ldots \ldots \ldots$
(A) a
(B) $2 \mathrm{a}$
(C) $(\mathrm{a} / \sqrt{2})$
(D) $(\mathrm{a} / \sqrt{3})$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:09

Problem 1535

Two identical charged spheres suspended from a common point by two massless strings of length $\ell$ are initially a distance d $(d<<\ell)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the spheres approach each other with a velocity $\mathrm{v}$. Then function of distance $\mathrm{x}$ between them becomes $\ldots \ldots$
(A) $v \propto x$
(B) $\mathrm{v} \propto \mathrm{x}^{(-1 / 2)}$
(C) $\mathrm{v} \propto \mathrm{x}^{-1}$
(D) $\mathrm{v} \propto \mathrm{x}^{(1 / 2)}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:07

Problem 1536

Three identical spheres each having a charge $\mathrm{q}$ and radius $R$, are kept in such a way that each touches the other two spheres. The magnitude of the electric force on any sphere due to other two is $\ldots \ldots \ldots$
(A) $(\mathrm{R} / 2)\left[1 /\left(4 \pi \epsilon_{0}\right)\right](\sqrt{5} / 4)(\mathrm{q} / \mathrm{R})^{2}$
(B) $\left[1 /\left(8 \pi \epsilon_{0}\right)\right](\sqrt{2} / 3)(\mathrm{q} / \mathrm{R})^{2}$
(C) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right](\sqrt{3} / 4)(\mathrm{q} / \mathrm{R})^{2}$
(D) $-\left[1 /\left(8 \pi \epsilon_{0}\right)\right](\sqrt{3} / 2)(\mathrm{q} / \mathrm{R})^{2}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:58

Problem 1537

Two equal negative charges $-q$ are fixed at points $(0, a)$ and $(0,-a)$ on the $\mathrm{Y}$ axis. A positive charge $q$ is released from rest at the point $x(x<<a)$ on the $X$ -axis, then the frequency of motion is ......
(B) $\left.\sqrt{[}\left(2 q^{2}\right) /\left(\pi \in_{0} m a^{3}\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:25

Problem 1538

Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases $4.5$ times in comparison with the initial value. The ratio of the initial charges of the balls is .......
(A) $4: 1$
(B) $6: 1$
(C) $3: 1$
(D) $2: 1$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:27

Problem 1539

A point charge $q$ is situated at a distance $r$ from one end of a thin conducting rod of length $\mathrm{L}$ having a charge $\mathrm{Q}$ (uniformly distributed along its length). The magnitude of electric force between the two, is ......
$(\mathrm{A})[(2 \mathrm{kqQ}) / \mathrm{r}(\mathrm{r}+\mathrm{L})]$
(B) $[(\mathrm{kq} \mathrm{Q}) / \mathrm{r}(\mathrm{r}+\mathrm{L})]$
(C) $[(\mathrm{kqQ}) / \mathrm{r}(\mathrm{r}-\mathrm{L})]$
(D) $[(\mathrm{kQ}) / \mathrm{r}(\mathrm{r}+\mathrm{L})]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:12

Problem 1540

Two point charges of $+16 \mathrm{c}$ and $-9 \mathrm{c}$ are placed $8 \mathrm{~cm}$ apart in air $\ldots \ldots$.. distance of a point from $-9$ c charge at which the resultant electric field is zero.
(A) $24 \mathrm{~cm}$
(B) $9 \mathrm{~cm}$
(C) $16 \mathrm{~cm}$
(D) $35 \mathrm{~cm}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:37

Problem 1541

Point charges $4 \mu \mathrm{c}$ and $2 \mu \mathrm{c}$ are placed at the vertices $\mathrm{P}$ and Q of a right angle triangle $P Q R$ respectively. $Q$ is the right angle, $\mathrm{PR}=2 \times 10^{-2} \mathrm{~m}$ and $\mathrm{QR}=10^{-2} \mathrm{~m}$. The magnitude and direction of the resultant electric field at $\mathrm{R}$ is $\ldots \ldots$
(A) $4.28 \times 10^{9} \mathrm{NC}^{-1}, 45^{\circ}$
(B) $2.38 \times 10^{8} \mathrm{NC}^{-1}, 40.9^{\circ}$
(C) $1.73 \times 10^{4} \mathrm{NC}^{-1}, 34.7^{\circ}$
(D) $4.9 \times 10^{10} \mathrm{NC}^{-1}, 34.7^{\circ}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:09

Problem 1542

An inclined plane making an angle of $30^{\circ}$ with the horizontal is placed in an uniform electric field $E=100 \mathrm{Vm}^{-1}$. A particle of mass $1 \mathrm{~kg}$ and charge $0.01 \mathrm{c}$ is allowed to slide down from rest from a height of $1 \mathrm{~m} .$ If the coefficient of friction is $0.2$ the time taken by the particle to reach the bottom is $\ldots \ldots . .$ sec
(A) $2.337$
(B) $4.337$
(C) 5
(D) $1.337$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:26

Problem 1543

A small sphere whose mass is $0.1 \mathrm{gm}$ carries a charge of $3 \times 10^{-10} \mathrm{C}$ and is tie up to one end of a silk fiber $5 \mathrm{~cm}$ long. The other end of the fiber is attached to a large vertical conducting plate which has a surface charge of $25 \times 10^{-6} \mathrm{Cm}^{-2}$, on each side. When system is freely hanging the angle fiber makes with vertical is $\ldots \ldots \ldots$
(A) $41.8^{\circ}$
(B) $45^{\circ}$
(C) $40.2^{\circ}$
(D) $45.8^{\circ}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:27

Problem 1544

A Semicircular rod is charged uniformly with a total charge $\mathrm{Q}$ coulomb. The electric field intensity at the centre of curvature is $\ldots \ldots \ldots$
(A) $\left[(2 \mathrm{KQ}) /\left(\pi \mathrm{R}^{2}\right)\right]$
(B) $\left[(3 \mathrm{KQ}) /\left(\pi \mathrm{R}^{2}\right)\right]$
(C) $\left[(\mathrm{KQ}) /\left(\pi \mathrm{R}^{2}\right)\right]$
(D) $\left[(4 \mathrm{KQ}) /\left(\pi \mathrm{R}^{2}\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:11

Problem 1545

The electron is projected from a distance $\mathrm{d}$ and with initial velocity vo parallel to a uniformly charged flat conducting plate as shown in figure. It strikes the plate after travelling a distance $\ell$ along the direction. The surface charge density of conducting plate is equal to
(A) $\left[\left(2 \mathrm{~d} \epsilon_{0} \mathrm{mv}_{0}\right) /(\mathrm{e} \ell)\right]$
(B) $\left[\left(\mathrm{d} \in{ }_{0} \mathrm{mv}_{0}{ }^{2}\right) /(\mathrm{e} \ell)\right]$
(C) $\left[\left(\mathrm{d} \in{ }_{0} \mathrm{mv}_{0}\right) /(\mathrm{e} \ell)\right]$
(D) $\left[\left(2 \mathrm{~d} \in{ }_{0} \mathrm{mv}_{0}^{2}\right) /\left(\mathrm{e} \ell^{2}\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:28

Problem 1546

Two point masses $\mathrm{m}$ each carrying charge $-\mathrm{q}$ and $+\mathrm{q}$ are attached to the ends of a massless rigid non-conducting rod of length $\ell$. The arrangement is placed in a uniform electric field $\mathrm{E}$ such that the rod makes a small angle $5^{\circ}$ with the field direction. The minimum time needed by the rod to align itself along the field is $\ldots \ldots .$
(A) $t=\pi \sqrt{[}(2 M \ell) /(3 q E)]$
(B) $\mathrm{t}=(\pi / 2) \sqrt{[}(\mathrm{M} \ell) /(2 \mathrm{q} \mathrm{E})]$
(D) $t=2 \pi \sqrt{[}(M \ell / E)]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:28

Problem 1547

Two uniformaly charged spherical conductors $\mathrm{A}$ and $\mathrm{B}$ having radius $1 \mathrm{~mm}$ and $2 \mathrm{~mm}$ are separated by a distance of $5 \mathrm{~cm} .$ If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $\mathrm{A}$ and $\mathrm{B}$ is.....
(A) $4: 1$
(B) $1: 2$
(C) $2: 1$
(D) $1: 4$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:59

Problem 1548

Let $\mathrm{P}(\mathrm{r})\left[\mathrm{Q} /\left(\pi \mathrm{R}^{4}\right)\right] \mathrm{r}$ be the charge density distribution for a solid sphere of radius $\mathrm{R}$ and total charge $\mathrm{Q}$. For a point ' $\mathrm{P}$ ' inside the sphere at distance $\mathrm{r}_{1}$ from the centre of the sphere the magnitude of electric field is
(A) $\left[\mathrm{Q} /\left(4 \pi \epsilon_{0} \mathrm{r}_{1}^{2}\right)\right]$
(B) $\left[\left(\mathrm{Qr}_{1}^{2}\right) /\left(4 \pi \in{ }_{0} \mathrm{R}^{4}\right)\right]$
(C) $\left[\left(\mathrm{Qr}_{1}^{2}\right) /\left(3 \pi \epsilon_{0} \mathrm{R}^{4}\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:14

Problem 1549

Two point charges $q_{1}=2 \mu c$ and $q_{2}=1 \mu c$ are placed at distance $\mathrm{b}=1 \mathrm{~cm}$ and $\mathrm{a}=2 \mathrm{~cm}$ from the origin on the $\mathrm{y}$ and $\mathrm{x}$ axes as shown in figure. The electric field vector at point $\mathrm{P}(\mathrm{a}, \mathrm{b})$ will subtend an angle $\theta$ with the $\mathrm{X}$ - axis given by,
(A) $\tan \theta=4$
(B) $\tan \theta=1$
(C) $\tan \theta=3$
(D) $\tan \theta=2$

Vysakh M
Vysakh M
Numerade Educator
01:12

Problem 1550

A simple pendulum consists of a small sphere of mass $\mathrm{m}$ suspended by a thread of length $\ell$. The sphere carries a positive charge q. The pendulum is placed in a uniform electric field of strength $\mathrm{E}$ directed Vertically upwards. If the electrostatic force acting on the sphere is less than gravitational force the period of pendulum is
(A) $\mathrm{T}=2 \pi[\ell /\{\mathrm{g}-(\mathrm{q} \mathrm{E} / \mathrm{m})\}]^{(1 / 2)}$
(B) $\mathrm{T}=2 \pi(\ell / \mathrm{g})^{(1 / 2)}$
$\left.\left.\left.\mathrm{m}_{\mathrm{}}\right\}\right\}\right]^{(1 / 2)}$
(D) $\mathrm{T}=2 \pi[(\mathrm{m} \ell / \mathrm{qE})]^{(1 / 2)}$
(C) $\mathrm{T}=2 \pi[\ell /\{\mathrm{g}+(\mathrm{qE} / \mathrm{t}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:53

Problem 1551

A simple pendulum consists of a small sphere of mass $\mathrm{m}$ suspended by a thread of length $\ell$. The sphere carries a positive charge q. The pendulum is placed in a uniform electric field of strength $\mathrm{E}$ directed Vertically upwards. If the electrostatic force acting on the sphere is less than gravitational force the period of pendulum is
(A) $\mathrm{T}=2 \pi[\ell /\{\mathrm{g}-(\mathrm{q} \mathrm{E} / \mathrm{m})\}]^{(1 / 2)}$
(B) $\mathrm{T}=2 \pi(\ell / \mathrm{g})^{(1 / 2)}$
$\left.\left.\left.\mathrm{m}_{\mathrm{}}\right\}\right\}\right]^{(1 / 2)}$
(D) $\mathrm{T}=2 \pi[(\mathrm{m} \ell / \mathrm{qE})]^{(1 / 2)}$
(C) $\mathrm{T}=2 \pi[\ell /\{\mathrm{g}+(\mathrm{qE} / \mathrm{t}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:09

Problem 1552

In Millikan's oil drop experiment an oil drop carrying a charge Q is held stationary by a p.d. $2400 \mathrm{v}$ between the plates. To keep a drop of half the radius stationary the potential difference had to be made $600 \mathrm{v}$. What is the charge on the second drop?
(A) $[(3 Q) / 2]$
(B) $(\mathrm{Q} / 4)$
(C) $Q$
(D) $(\mathrm{Q} / 2)$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:48

Problem 1553

Equal charges $q$ are placed at the vertices $A$ and $B$ of an equilateral triangle $\mathrm{ABC}$ of side $\mathrm{a}$. The magnitude of electric field at the point $c$ is $\ldots \ldots \ldots$
(A) $\left(\mathrm{Kq} / \mathrm{a}^{2}\right)$
(B) $\left.(\sqrt{3} \mathrm{Kq}) / \mathrm{a}^{2}\right)$
(C) $\left.(\sqrt{2} \mathrm{Kq}) / \mathrm{a}^{2}\right)$
(D) $\left[\mathrm{q} /\left(2 \pi \mathrm{t} \varepsilon_{0} \mathrm{a}^{2}\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:34

Problem 1554

An electric dipole is placed along the $\mathrm{x}$ -axis at the origin o. $\mathrm{A}$ point $P$ is at a distance of $20 \mathrm{~cm}$ from this origin such that OP makes an angle $(\pi / 3)$ with the x-axis. If the electric field at P makes an angle $\theta$ with the x-axis, the value of $\theta$ would be $\ldots \ldots \ldots$
(A) $(\pi / 3)+\tan ^{-1}(\sqrt{3} / 2)$
(B) $(\pi / 3)$
(C) $(2 \pi / 3)$
(D) $\tan ^{-1}(\sqrt{3} / 2)$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:00

Problem 1555

A particle having a charge of $1.6 \times 10^{-19} \mathrm{C}$ enters between the plates of a parallel plate capacitor. The initial velocity of the particle is parallel to the plates. A potential difference of $300 \mathrm{v}$ is applied to the capacitor plates. If the length of the capacitor plates is $10 \mathrm{~cm}$ and they are separated by $2 \mathrm{~cm}$, Calculate the greatest initial velocity for which the particle will not be able to come out of the plates. The mass of the particle is $12 \times 10^{-24} \mathrm{~kg}$.
(A) $10^{4}(\mathrm{~m} / \mathrm{s})$
(B) $10^{2}(\mathrm{~m} / \mathrm{s})$
(C) $10^{-1}(\mathrm{~m} / \mathrm{s})$
(D) $10^{3}(\mathrm{~m} / \mathrm{s})$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:18

Problem 1556

A charged particle of mass $1 \mathrm{~kg}$ and charge $2 \mu \mathrm{c}$ is thrown from a horizontal ground at an angle $\theta=45^{\circ}$ with speed $20 \mathrm{~m} / \mathrm{s}$. In space a horizontal electric field $\mathrm{E}=2 \times 10^{7} \mathrm{~V} / \mathrm{m}$
exist. The range on horizontal ground of the projectile thrown is $\ldots \ldots \ldots$
(A) $100 \mathrm{~m}$
(B) $50 \mathrm{~m}$
(C) $200 \mathrm{~m}$
(D) $0 \mathrm{~m}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:00

Problem 1556

The capacities of three capacitors are in the ratio $1: 2: 3$. Their equivalent capacity when connected in parallel is $(60 / 11) \mathrm{F}$ more then that when they are connected in series. The individual capacitors are of capacities in $\mu \mathrm{F}$
(A) $4,6,7$
(B) $1,2,3$
(C) $1,3,6$
(D) $2,3,4$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:10

Problem 1557

If electron in ground state of $\mathrm{H}$ -atom is assumed in rest then dipole moment of electron proton system of $\mathrm{H}$ -atom is $\ldots \ldots$ Orbit radius of $\mathrm{H}$ atom in ground state is $0.56 \AA$.
(A) $0.253 \times 10^{-29} \mathrm{~m}$
(B) $0.848 \times 10^{-29} \mathrm{~m}$
(C) $0.305 \times 10^{-29} \mathrm{~m}$
(D) $1.205 \times 10^{-28} \mathrm{~m}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:57

Problem 1557

In the given arrangement of capacitors equivalent capacitance between points $\mathrm{M}$ and $\mathrm{N}$ is
(A) $(5 / 4) \mathrm{C}$
(B) $(4 / 5) \mathrm{C}$
(C) $(4 / 3) \mathrm{C}$
(D) $(3 / 4) \mathrm{C}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:54

Problem 1558

At what angle $\theta$ a point $P$ must be located from dipole axis so that the electric field intensity at the point is perpendicular to the dipole axis?
(A) $\tan ^{-1}(1 / \sqrt{2})$
(B) $\tan ^{-1}(1 / 2)$
(C) $\tan ^{-1}(2)$
(C) $\tan ^{-1}(\sqrt{2})$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:28

Problem 1559

An electric dipole is placed at an angle of $60^{\circ}$ with an electric field of intensity $10^{5} \mathrm{NC}^{-1}$. It experiences a torque equal to $8 \sqrt{3} \mathrm{Nm}$. If the dipole length is $2 \mathrm{~cm}$ then the charge on the dipole is $\ldots \ldots \ldots$ c.
(A) $-8 \times 10^{3}$
(B) $8.54 \times 10^{-4}$
(C) $8 \times 10^{-3}$
(D) $0.85 \times 10^{-6}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:27

Problem 1560

An electric dipole coincides on $z$ axis and its mid point is on origin of the cartesian co-ordinate system. The electric field at an axial point at a distance $z$ from origin is $E^{-}(z)$ and electric field at an equatorial point at a distance y from origin is $E^{\rightarrow}$ (y) $\left|E^{-}(z) / E^{-}(y)\right|(y=z \gg>a)=\ldots \ldots \ldots .$
(A) 1
(B) 2
(C) 4
(D) 3

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:03

Problem 1561

An oil drop of 12 excess electrons is held stationary under a constant electric field of $2.55 \times 10^{4} \mathrm{Vm}^{-1}$. If the density of the oil is $1.26 \mathrm{gm} / \mathrm{cm}^{3}$ then the radius of the drop is $\ldots \ldots \ldots \mathrm{m}$.
(A) $9.75 \times 10^{-7}$
(B) $9.29 \times 10^{-7}$
(C) $9.38 \times 10^{-8}$
(D) $9.34 \times 10^{-8}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:52

Problem 1562

A Charge $q$ is placed at the centre of the open end of cylindrical vessel. The flux of the electric field through the surface of the vessel is $\ldots \ldots \ldots \ldots$
(A) $\left(\mathrm{q} / \in_{0}\right)$
(B) (q / $2 \in_{0}$ )
(C) $\left(2 q / \epsilon_{0}\right)$
(D) Zero

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:14

Problem 1563

The inward and outward electric flux for a closed surface in units of $\mathrm{Nm}^{2} / \mathrm{C}$ are respectively $8 \times 10^{3}$ and $4 \times 10^{3}$. Then the total charge inside the surface is $\ldots \ldots \ldots \ldots . . \mathrm{c}$.
(A) $\left[\left(-4 \times 10^{3}\right) / \epsilon_{0}\right]$
(B) $-4 \times 10^{3}$
(C) $4 \times 10^{3}$
(D) $-4 \times 10^{3} \mathrm{E}_{0}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:25

Problem 1564

A sphere of radius $R$ has a uniform distribution of electric charge in its volume. At a distance $\mathrm{x}$ from its centre, (for $\mathrm{x}<\mathrm{R})$, the electric field is directly proportional to ......
(A) $\mathrm{x}$
(B) $\mathrm{x}^{-1}$
(C) $x^{-2}$
(D) $\mathrm{x}^{2}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:14

Problem 1565

The electric flux for gaussian surface $\mathrm{A}$ that enclose the $\ldots \ldots$ charged particles in free space is (given $\left.q_{1}=-14 n c, q_{2}=78.85 \mathrm{nc}, q_{3}=-56 n c\right)$
(A) $10^{4} \mathrm{Nm}^{2} / \mathrm{C}$
(B) $10^{3} \mathrm{Nm}^{2} / \mathrm{C}$
(C) $6.2 \times 10^{3} \mathrm{Nm}^{2} / \mathrm{C}$
(D) $6.3 \times 10^{4} \mathrm{Nm}^{2} / \mathrm{C}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:41

Problem 1566

A hollow cylinder has a charge q coulomb within it. If $\Phi$ is the electric flux in units of voltmeter associated with the curved surface $\mathrm{B}$, the flux linked with the plane surface $\mathrm{A}$ in units of volt-meter will be $\ldots \ldots \ldots$
$(\mathrm{A})(1 / 2)\left[\left(\mathrm{q} / \mathrm{\epsilon}_{0}\right)-\Phi\right]$
(B) $\left[\left(\mathrm{q} / 2 \mathrm{e}_{0}\right)\right.$
(C) $(\Phi / 3)$
(D) $\left(\mathrm{q} / \epsilon_{0}\right)-\Phi$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:56

Problem 1567

An infinitely long thin straight wire has uniform linear charge density of $(1 / 3) \mathrm{c} / \mathrm{m}$. Then, the magnitude of the electric intensity at a point $18 \mathrm{~cm}$ away is $\ldots \ldots . \mathrm{NC}^{-1}$.
(A) $0.66 \times 10^{11}$
(B) $1.32 \times 10^{11}$
(C) $0.33 \times 10^{11}$
(D) $3 \times 10^{11}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:38

Problem 1568

Iwo points are at distances a and b $(a<b)$ from a long string of charge per unit length $\lambda$. The potential difference between the points in proportional to $\ldots \ldots \ldots$
(A) $\ln (\mathrm{b} / \mathrm{a})$
(B) $\left[\lambda /\left(\pi \epsilon_{0}\right)\right] \ln \left(b^{2} / a^{2}\right)$
(C) $\left[\lambda /\left(2 \pi \epsilon_{0}\right)\right] \ln \sqrt{(b / a)}$
(D) $\left[\lambda /\left(2 \pi \epsilon_{0}\right)\right] \ln (\mathrm{b} / \mathrm{a})$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:15

Problem 1569

A long string with a charge of $\lambda$ per unit length passes through an imaginary cube of edge $\ell$. The maximum possible flux of the electric field through the cube will be .......
(A) $\sqrt{3}\left(\lambda \ell / \in_{0}\right)$
(B) $\left(\lambda \ell / \in_{0}\right)$
(C) $\sqrt{2}\left(\lambda \ell / \in_{0}\right)$
(D) $\left[\left(6 \lambda \ell^{2}\right) / \epsilon_{0}\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:40

Problem 1570

Two Points $P$ and $Q$ are maintained at the Potentials of $10 \mathrm{v}$ and $-4 \mathrm{v}$, respectively. The work done in moving 100 electrons from $\mathrm{P}$ to $\mathrm{Q}$ is $\ldots \ldots \ldots$
(A) $2.24 \times 10^{-16} \mathrm{~J}$
(B) $-9.60 \times 10^{-17} \mathrm{~J}$
(C) $-2.24 \times 10^{-16} \mathrm{~J}$
(D) $9.60 \times 10^{-17} \mathrm{~J}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:15

Problem 1571

The electric Potential $\mathrm{V}$ at any Point $0(\mathrm{x}, \mathrm{y}, \mathrm{z}$ all in meters $)$ in space is given by $\mathrm{V}=4 \mathrm{x}^{2}$ volt. The electric field at the point $(1 \mathrm{~m}, 0.2 \mathrm{~m})$ in volt meter is $\ldots \ldots .$
(A) 8 , along negative $\mathrm{x}$ - axis
(B) 8 , along positives $\mathrm{x}$ - axis
(C) 16 , along negative $\mathrm{x}$ -axis
(D) 16 , along positives $\mathrm{x}$ -axis

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:19

Problem 1572

Charges of $+(10 / 3) \times 10^{-9} \mathrm{C}$ are placed at each of the four corners of a square of side $8 \mathrm{~cm}$. The potential at the intersection of the diagonals is ......
(A) $150 \sqrt{2}$ Volt
(B) $900 \sqrt{2}$ Volt
(C) $1500 \sqrt{2}$ Volt
(D) $900 \sqrt{2} \cdot \sqrt{2}$ Volt

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:13

Problem 1573

Three charges $2 q,-q,-q$ are located at the vertices of an equilateral triangle. At the centre of the triangle.
(A) The Field is Zero but Potential is non - zero
(B) The Field is non - Zero but Potential is zero
(C) Both field and Potential are Zero
(D) Both field and Potential are non - Zero

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:52

Problem 1574

In the electric field of a point charge $q$, a certain charge is carried from point $\mathrm{A}$ to $\mathrm{B}, \mathrm{C}, \mathrm{D}$ and $\mathrm{E}$. Then the work done $\ldots \ldots$
(A) Is least along the Path AB
(B) Is least along the Path AD
(C) Is Zero along all the Path $\mathrm{AB}, \mathrm{AC}$, and $\mathrm{AD}, \mathrm{AE}$.
(D) Is least along $\mathrm{AE}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:13

Problem 1575

Three concentric spherical shells have radii a, $b$ and $c(a<b<c)$ and have surface charge densities $\sigma,-\sigma$ and $\sigma$ respectively. If $\mathrm{V}_{\mathrm{A}}, \mathrm{V}_{\mathrm{B}}$ and $\mathrm{V}_{\mathrm{C}}$ denote the Potentials of the three shells, then for $\mathrm{c}=\mathrm{a}+\mathrm{b}$, we have
(A) $\mathrm{V}_{\mathrm{C}}=\mathrm{V}_{\mathrm{B}}=\mathrm{V}_{\mathrm{A}}$
(B) $\mathrm{V}_{\mathrm{C}}=\mathrm{V}_{\mathrm{B}} \neq \mathrm{V}_{\mathrm{A}}$
(C) $\mathrm{V}_{\mathrm{C}}=\mathrm{V}_{\mathrm{B}} \neq \mathrm{V}_{\mathrm{A}}$
(D) $\mathrm{V}_{\mathrm{C}}=\mathrm{V}_{\mathrm{A}} \neq \mathrm{V}_{\mathrm{B}}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:34

Problem 1576

The electric Potential at a point $\mathrm{P}(\mathrm{x}, \mathrm{y}, \mathrm{z})$ is given by $\mathrm{V}=-\mathrm{x}^{2} \mathrm{y}-\mathrm{x} \mathrm{z}^{3}+4$. The electric field $\mathrm{E}^{\boldsymbol{T}}$ at that point is $\ldots \ldots$
(A) $i \wedge\left(2 \mathrm{xy}+\mathrm{z}^{3}\right)+\mathrm{j} \wedge \mathrm{x}^{2}+\mathrm{k} \wedge 3 \mathrm{xz}^{2}$
(B) $i \wedge 2 \mathrm{xy}+\mathrm{j} \wedge\left(\mathrm{x}^{2}+\mathrm{y}^{2}\right)+\mathrm{k} \wedge\left(3 \mathrm{xy}-\mathrm{y}^{2}\right)$
(C) $i \wedge z^{3}+j \wedge x y z+k \wedge z^{2}$
(D) $i \wedge\left(2 x y-z^{3}\right)+j \wedge x y^{2}+k \wedge 3 z^{2} x$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:59

Problem 1577

Three particles, each having a charge of $10 \mu \mathrm{c}$ are placed at the corners of an equilateral triangle of side $10 \mathrm{~cm}$. The electrostatic potential energy of the system is (Given $\left.\left[1 /\left(4 \pi \epsilon_{0}\right)\right]=9 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{c}^{2}\right)$
(A) $100 \mathrm{~J}$
(B) $27 \mathrm{~J}$
(C) Zero
(D) Infinite

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:26

Problem 1578

Four equal charges $\mathrm{Q}$ are placed at the four corners of a square of each side is ' $\mathrm{a}$ '. Work done in removing a charge
- Q from its centre to infinity is .......
(A) 0
(B) $\left[\left(\sqrt{2} \mathrm{Q}^{2}\right) /\left(\pi \epsilon_{0} \mathrm{a}\right)\right]$
(C) $\left[\left(\sqrt{2} Q^{2}\right) /\left(4 \pi \epsilon_{0} a\right)\right]$
(D) $\left[\mathrm{Q}^{2} /\left(2 \pi \epsilon_{0} \mathrm{a}\right)\right]$

Vishal Gupta
Vishal Gupta
Numerade Educator
01:00

Problem 1579

Two charged spheres of radii $R_{1}$ and $R_{2}$ having equal surface charge density. The ratio of their potential is .....
(A) $\left(\mathrm{R}_{2} / \mathrm{R}_{1}\right)$
(B) $\left(\mathrm{R}_{2} / \mathrm{R}_{1}\right)^{2}$
(C) $\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)^{2}$
(D) $\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:13

Problem 1580

Two equal charges $q$ are placed at a distance of $2 \mathrm{a}$ and a third charge $-2 q$ is placed at the midpoint. The potential energy of the system is .......
(A) $\left[\left(9 \mathrm{q}^{2}\right) /\left(8 \pi \epsilon_{0} \mathrm{a}\right)\right]$
(B) $\left[q^{2} /\left(8 \pi \epsilon_{0} a\right)\right]$
(C) $-\left[\left(7 q^{2}\right) /\left(8 \pi \epsilon_{0} a\right)\right]$
(D) $\left[\left(6 q^{2}\right) /\left(8 \pi \in_{0} a\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:25

Problem 1581

Two point charges $100 \mu \mathrm{c}$ and $5 \mu \mathrm{c}$ are placed at points $\mathrm{A}$ and $B$ respectively with $A B=40 \mathrm{~cm}$. The work done by external force in displacing the charge $5 \mu \mathrm{c}$ from $\mathrm{B}$ to $\mathrm{C}$ where $\mathrm{BC}=30 \mathrm{~cm}$, angle $\mathrm{ABC}=(\pi / 2)$ and $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]$
$=9 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{c}^{2}$.
(A) $9 \mathrm{~J}$
(B) $(9 / 25) \mathrm{J}$
(C) $(81 / 20) \mathrm{J}$
(D) $-(9 / 4) \mathrm{J}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:48

Problem 1582

The electric potential $\mathrm{V}$ is given as a function of distance $\mathrm{x}$ (meter) by $\mathrm{V}=\left(5 \mathrm{x}^{2}+10 \mathrm{x}-9\right)$ volt. Value of electric field at $\mathrm{x}=1$ is $\ldots \ldots$
$(\mathrm{A})-20(\mathrm{v} / \mathrm{m})$
(B) $6(\mathrm{v} / \mathrm{m})$
(C) $11(\mathrm{v} / \mathrm{m})$
(D) $-23(\mathrm{v} / \mathrm{m})$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:08

Problem 1583

A sphere of radius $1 \mathrm{~cm}$ has potential of $8000 \mathrm{v}$, then energy density near its surface will be ......
(A) $64 \times 10^{5}\left(\mathrm{~J} / \mathrm{m}^{3}\right)$
(B) $2.83\left(\mathrm{~J} / \mathrm{m}^{3}\right)$
(C) $8 \times 10^{3}\left(\mathrm{~J} / \mathrm{m}^{3}\right)$
(D) $32\left(\mathrm{~J} / \mathrm{m}^{3}\right)$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:16

Problem 1584

If a charged spherical conductor of radius $10 \mathrm{~cm}$ has potential $\mathrm{v}$ at a point distant $5 \mathrm{~cm}$ from its centre, then the potential at a point distant $15 \mathrm{~cm}$ from the centre will be $\ldots . .$
(A) $(1 / 3) \mathrm{V}$
(B) $(3 / 2) \mathrm{V}$
(C) $3 \mathrm{~V}$
(D) $(2 / 3) \mathrm{V}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:50

Problem 1585

Electric charges of $+10 \mu \mathrm{c}, 5 \mu \mathrm{c},-3 \mu \mathrm{c}$ and $8 \mu \mathrm{c}$ are placed at the corners of a square of side $\sqrt{2 m}$ the potential at the centre of the square is $\ldots \ldots$
(A) $1.8 \mathrm{~V}$
(B) $1.8 \times 10^{5} \mathrm{~V}$
(C) $1.8 \times 10^{6} \mathrm{~V}$
(D) $1.8 \times 10^{4} \mathrm{~V}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:19

Problem 1586

Two positive point charges of $12 \mu \mathrm{c}$ and $8 \mu \mathrm{c}$ are $10 \mathrm{~cm}$ apart each other. The work done in bringing them $4 \mathrm{~cm}$ closer is ....
(A) $5.8 \mathrm{~J}$
(B) $13 \mathrm{eV}$
(C) $5.8 \mathrm{eV}$
(D) $13 \mathrm{~J}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:23

Problem 1587

The displacement of a charge $Q$ in the electric field $E^{-}=e_{1} i \wedge+e_{2} j \wedge+e_{3} k \wedge$ is $r^{-}=a i \wedge+b j \wedge$
The work done is $\ldots \ldots$
(A) $Q\left(e_{1}+e_{2}\right) \sqrt{\left(a^{2}+b^{2}\right)}$
(B) $Q\left[\sqrt{ \left.\left(e_{1}^{2}+e_{2}^{2}\right)\right](a+b)}\right.$
(C) $Q\left(a e_{1}+b e_{2}\right)$
(D) $\left.Q \sqrt{[}\left(a e_{1}\right)^{2}+\left(b e_{2}\right)^{2}\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:16

Problem 1588

If an electron moves from rest from a point at which potential is 50 volt, to another point at which potential is 70 volt, then its kinetic energy in the final state will be $\ldots .$
(A) $1 \mathrm{~N}$
(B) $3.2 \times 10^{-18} \mathrm{~J}$
(C) $3.2 \times 10^{-10} \mathrm{~J}$
(D) 1 dyne

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:49

Problem 1589

Three charges $\mathrm{Q},+\mathrm{q}$ and $+\mathrm{q}$ are placed at the verticals of a right-angled triangle as shown. The net electrostatic energy of the configuration is zero if $Q$ is equal to $\ldots \ldots .$
(A) $-2 \mathrm{q}$
(B) $[-q /(1+\sqrt{2})]$
(C) $+q$
(D) $[(-2 q) /(2+\sqrt{2})]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:16

Problem 1590

Two electric charges $12 \mu \mathrm{c}$ and $-6 \mu \mathrm{c}$ are placed $20 \mathrm{~cm}$ apart in air. There will be a point $P$ on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of $P$ from $-6 \mu c$ charge is .....
(A) $0.20 \mathrm{~m}$
(B) $0.10 \mathrm{~m}$
(C) $0.25 \mathrm{~m}$
(D) $0.15 \mathrm{~m}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:48

Problem 1591

If the rectangle, shown below, the two corners have charges $q_{1}=-5 \mu c$ and $q_{2}=+2.0 \mu c .$ The work done in moving a charge $3 \mu c$ from $\mathrm{B}$ to $\mathrm{A}$ is $\left[\right.$ taken $\left.\left[1 /\left(4 \pi \epsilon_{0}\right)\right]=10^{10} \mathrm{Nm}^{2} / \mathrm{c}^{2}\right]$.
(A) $5.5 \mathrm{~J}$
(B) $2.5 \mathrm{~J}$
(C) $3.5 \mathrm{~J}$
(D) $4.5 \mathrm{~J}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:00

Problem 1592

4 Points charges each $+q$ is placed on the circumference of a circle of diameter $2 \mathrm{~d}$ in such a way that they form a square. The potential at the centre is $\ldots \ldots .$
(A) 0
(B) $(4 \mathrm{kd} / \mathrm{q})$
(C) $(\mathrm{kd} / 4 \mathrm{q})$
(D) $(4 \mathrm{kq} / \mathrm{d})$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:19

Problem 1593

Three identical charges each of $2 \mu \mathrm{c}$ are placed at the vertices of a triangle $A B C$ as shown in the figure. If $\mathrm{AB}+\mathrm{AC}=12 \mathrm{~cm}$ and $\mathrm{AB} \cdot \mathrm{AC}=32 \mathrm{~cm}^{2}$, the potential energy
of the charge at $\mathrm{A}$ is $\ldots \ldots$
(A) $1.53 \mathrm{~J}$
(B) $5.31 \mathrm{~J}$
(C) $1.35 \mathrm{~J}$
(D) $3.15 \mathrm{~J}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:02

Problem 1594

A ball of mass $1 \mathrm{gm}$ and charge $10^{-8} \mathrm{c}$ moves from a point $\mathrm{A}$, where the potential is 600 volt to the point $B$ where the potential is zero. Velocity of the ball of the point $\mathrm{B}$ is $20 \mathrm{~cm} / \mathrm{s}$. The velocity of the ball at the point $\mathrm{A}$ will be $\ldots \ldots$
(A) $16.8(\mathrm{~m} / \mathrm{s})$
(B) $22.8(\mathrm{~cm} / \mathrm{s})$
(C) $228(\mathrm{~cm} / \mathrm{s})$
(D) $168(\mathrm{~m} / \mathrm{s})$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:42

Problem 1595

Three charges $\mathrm{Q},+\mathrm{q}$ and $+\mathrm{q}$ are placed at the vertices of an equilateral triangle of side $\ell$ as shown in the figure. It the net electrostatic energy of the system is zero, then $Q$ is equal
(A) $-\mathrm{q}$
(B) $+q$
(C) Zero
(D) $-(q / 2)$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:51

Problem 1596

Electric potential at any point is $\mathrm{V}=-5 \mathrm{x}+3 \mathrm{y}+\sqrt{(15 \mathrm{z})}$, then the magnitude of the electric field is $\ldots \ldots \ldots \mathrm{N} / \mathrm{C}$.
(A) $3 \sqrt{2}$
(B) $4 \sqrt{2}$
(C) 7
(D) $5 \sqrt{2}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:11

Problem 1597

A small conducting sphere of radius $r$ is lying concentrically inside a bigger hollow conducting sphere of radius $R$. The bigger and smaller sphere are charged with $\mathrm{Q}$ and $\mathrm{q}(\mathrm{Q}>\mathrm{q})$ and are insulated from each other. The potential difference between the spheres will be $\ldots \ldots$
(A) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right][(q / r)-(Q / R)]$
(B) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right][(q / r)-(q / R)]$
(C) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right][(Q / R)+(q / r)]$
(D) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right][(\mathrm{q} / \mathrm{R})-(\mathrm{Q} / \mathrm{r})]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:38

Problem 1598

If 3 charges are placed at the vertices of equilateral triangle of charge ' $q$ ' each. What is the net potential energy, if the side of equilateral triangle is $\ell \mathrm{cm}$.
(A) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(3 q^{2} / \ell\right)$
(B) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(2 q^{2} / \ell\right)$
(C) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(q^{2} / \ell\right)$
(D) $\left[1 /\left(4 \pi \epsilon_{0}\right)\right]\left(4 q^{2} / \ell\right)$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:50

Problem 1599

If identical charges $(-q)$ are placed at each corner of a cube of side $b$, then electric potential energy of charge $(+q)$ which is placed at centre of the cube will be .....
(A) $-\left[\left(4 q^{2}\right) /\left(\sqrt{3} \pi \epsilon_{0} b\right)\right]$
(B) $\left[\left(8 \sqrt{2} \mathrm{q}^{2}\right) /\left(4 \pi \epsilon_{0} \mathrm{~b}\right)\right]$
(C) $\left[\left(-8 \sqrt{2} q^{2}\right) /\left(\pi \in_{0} b\right)\right]$
(D) $\left[\left(-4 \sqrt{2 q^{2}}\right) /\left(4 \pi \epsilon_{0} b\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:58

Problem 1600

A simple pendulum of period $\mathrm{T}$ has a metal bob which is negatively charged. If it is allowed to oscillate above a positively charged metal plate, its period will ......
(A) Remains equal to $\mathrm{T}$
(B) Less than $\mathrm{T}$
(C) Infinite
(D) Greater than $\mathrm{T}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:09

Problem 1601

A charged particle of mass $\mathrm{m}$ and charge $q$ is released from rest in a uniform electric field $E$. Neglecting the effect of gravity, the kinetic energy of the charged particle after 't' second is ......
(A) $\left[\left(\mathrm{Eq}^{2} \mathrm{~m}\right) /\left(2 \mathrm{t}^{2}\right)\right]$
(B) $\left[\left(\mathrm{E}^{2} \mathrm{q}^{2} \mathrm{t}^{2}\right) /(2 \mathrm{~m})\right]$
(C) $\left[\left(2 \mathrm{E}^{2} \mathrm{t}^{2}\right) /(\mathrm{qm})\right]$
(D) $[(\mathrm{Eqm}) / \mathrm{t}]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:52

Problem 1602

A thin spherical conducting shell of radius $\mathrm{R}$ has a charge q. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point p a distance $(\mathrm{R} / 2)$ from the centre of the shell is .....
(A) $\left[(q+Q) /\left(4 \pi \epsilon_{0}\right)\right](2 / R)$
(B) $\left[\left\{(2 Q) /\left(4 \pi \epsilon_{0} R\right)\right\}-\left\{(2 Q) /\left(4 \pi \epsilon_{0} R\right)\right]\right.$
(C) $\left[\left\{(2 Q) /\left(4 \pi \in_{0} R\right)\right\}+\left\{q /\left(4 \pi \epsilon_{0} R\right)\right]\right.$
(D) $\left[(2 \mathrm{Q}) /\left(4 \pi \epsilon_{0} \mathrm{R}\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:12

Problem 1603

Two point charges $-q$ and $+q$ are located at points $(0,0,-a)$ and $(0,0, a)$ respectively. The potential at a point $(0,0, z)$ where $z>a$ is $\ldots \ldots$
(A) $\left[(2 \mathrm{q} a) /\left\{4 \pi \epsilon_{0}\left(z^{2}+a^{2}\right)\right\}\right]$
(B) $\left[\mathrm{q} /\left(4 \pi \epsilon_{0} \mathrm{a}\right)\right]$
(C) $\left[\right.$ (qa) $\left./\left(4 \pi \in_{0} z^{2}\right)\right]$
(D) $\left[(2 q a) /\left\{4 \pi \epsilon_{0}\left(z^{2}-a^{2}\right)\right\}\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:34

Problem 1604

Point charges $q_{1}=2 \mu c$ and $q_{2}=-1 \mu c$ care kept at points $\mathrm{x}=0$ and $\mathrm{x}=6$ respectively. Electrical potential will be zero at points .....
(A) $\mathrm{x}=-2, \mathrm{x}=2$
(B) $\mathrm{x}=1, \mathrm{x}=5$
(C) $\mathrm{x}=4, \mathrm{x}=12$
(D) $\mathrm{x}=2, \mathrm{x}=9$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:25

Problem 1605

Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $+q$ and $-q$. The potential difference between the centers of the two rings is $\ldots .$
(A) 0
(B) $\left.\left[\mathrm{q} /\left(2 \pi \epsilon_{0}\right)\right]\left[(1 / \mathrm{R})-\left\{1 / \sqrt{(}^{2}+\mathrm{d}^{2}\right)\right\}\right]$
(C) $\left[\mathrm{q} /\left(4 \pi \epsilon_{0}\right)\right]\left[(1 / \mathrm{R})-\left\{1 / \sqrt{\left. \left.\left(\mathrm{R}^{2}+\mathrm{d}^{2}\right)\right\}\right]}\right.\right.$
(D) $\left[(q R) /\left(4 \pi \epsilon_{0} d^{2}\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:51

Problem 1606

Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $+q$ and $-q$. The potential difference between the centers of the two rings is $\ldots .$
(A) 0
(B) $\left.\left[\mathrm{q} /\left(2 \pi \epsilon_{0}\right)\right]\left[(1 / \mathrm{R})-\left\{1 / \sqrt{(}^{2}+\mathrm{d}^{2}\right)\right\}\right]$
(C) $\left[\mathrm{q} /\left(4 \pi \epsilon_{0}\right)\right]\left[(1 / \mathrm{R})-\left\{1 / \sqrt{\left. \left.\left(\mathrm{R}^{2}+\mathrm{d}^{2}\right)\right\}\right]}\right.\right.$
(D) $\left[(q R) /\left(4 \pi \epsilon_{0} d^{2}\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:49

Problem 1607

Figure shows a triangular array of three point charges. The electric potential $\mathrm{V}$ of these source charges at the midpoint $\mathrm{P}$ of the base of the triangle is $\left[1 /\left(4 \pi \epsilon_{0}\right)=9 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{c}^{2}\right]$
(A) $55 \mathrm{KV}$
(B) $63 \mathrm{KV}$
(C) $49 \mathrm{KV}$
(D) $45 \mathrm{KV}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:37

Problem 1608

Charges $+q$ and $-q$ are placed at point $A$ and $B$ respectively which are a distance $2 \mathrm{~L}$ apart, $\mathrm{C}$ is the midpoint between $\mathrm{A}$ and $\mathrm{B}$. The work done in moving a charge $+Q$ along the semicircle $C R D$ is $\ldots \ldots$
(A) $\left[(\mathrm{qQ}) /\left(2 \pi \mathrm{\epsilon}_{0} \mathrm{~L}\right)\right]$
(B) $\left[(-q Q) /\left(6 \pi \in_{0} L\right)\right]$
(C) $\left[(\mathrm{qQ}) /\left(6 \pi \mathrm{e}_{0} \mathrm{~L}\right)\right]$
(D) $\left[(q Q) /\left(4 \pi \in_{0} L\right)\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:32

Problem 1609

N identical drops of mercury are charged simultaneously to 10 volt. when combined to form one large drop, the potential is found to be 40 volt, the value of $\mathrm{N}$ is $\ldots \ldots$
(A) 4
(B) 6
(C) 8
(D) 10

Vysakh M
Vysakh M
Numerade Educator
01:08

Problem 1610

Two parallel plate air capacitors have their plate areas 100 and $500 \mathrm{~cm}^{2}$ respectively. If they have the same charge and potential and the distance between the plates of the first capacitor is $0.5 \mathrm{~mm}$, what is the distance between the plates of the second capacitor ?
(A) $0.25 \mathrm{~cm}$
(B) $0.50 \mathrm{~cm}$
(C) $0.75 \mathrm{~cm}$
(D) $1 \mathrm{~cm}$

Narayan Hari
Narayan Hari
Numerade Educator
01:17

Problem 1611

The eftective capacitances of two capacitors are $3 \mu \mathrm{F}$ and $16 \mu \mathrm{F}$, when they are connected in series and parallel respectively. The capacitance of each capacitor is
(A) $2 \mu \mathrm{F}, 14 \mu \mathrm{F}$
(B) $4 \mu \mathrm{F}, 12 \mu \mathrm{F}$
(C) $6 \mu \mathrm{F}, 8 \mu \mathrm{F}$
(D) $10 \mu \mathrm{F}, 6 \mu \mathrm{F}$

Narayan Hari
Narayan Hari
Numerade Educator
03:51

Problem 1612

An electrical technician requires a capacitance of $2 \mu \mathrm{F}$ in a circuit across a potential difference of $1 \mathrm{KV}$. A large number of $1 \mu \mathrm{F}$ capacitors are available to him, each of which can withstand a potential difference of not than $400 \mathrm{~V}$. suggest a possible arrangement that requires a minimum number of capacitors.
(A) 2 rows with 2 capacitors
(B) 4 rows with 2 capacitors
(C) 3 rows with 4 capacitors
(D) 6 rows with 3 capacitors

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:06

Problem 1613

Two spherical conductors of radii $\mathrm{r}_{1}$ and $\mathrm{r}_{2}$ are at potentials $\mathrm{v}_{1}$ and $\mathrm{v}_{2}$ respectively, then what will be the common potential when the conductors are brought in constant?
(A) $\left[\left(\mathrm{r}_{1} \mathrm{v}_{1}+\mathrm{r}_{2} \mathrm{v}_{2}\right) /\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)\right]$
(B) $\left[\left(\mathrm{r}_{1} \mathrm{v}_{1}+\mathrm{r}_{2} \mathrm{v}_{2}\right) /\left(\mathrm{r}_{1}-\mathrm{r}_{2}\right)\right]$
(C) $\left[\left(\mathrm{r}_{1} \mathrm{v}_{1}-\mathrm{r}_{2} \mathrm{v}_{2}\right) /\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)\right]$
(D) None of these

Narayan Hari
Narayan Hari
Numerade Educator
01:30

Problem 1614

A $5 \mu \mathrm{F}$ capacitor is charged by a $220 \mathrm{v}$ supply. It is then disconnected from the supply and is connected to another uncharged $2.5 \mu \mathrm{F}$ capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation ?
(A) $0.02 \mathrm{~J}$
(B) $0.121 \mathrm{~J}$
(C) $0.04 \mathrm{~J}$
(D) $0.081 \mathrm{~J}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:05

Problem 1615

Find the equivalent capacitance of the system across the terminals $\mathrm{A}$ and $\mathrm{B}$. All the capacitors have equal capacitances.
(A) $2 \mathrm{C}$
(B) $4 \mathrm{C}$
(C) $3 \mathrm{C}$
(D) $5 \mathrm{C}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:29

Problem 1616

Capacitance of a parallel plate capacitor becomes $(4 / 3)$ times its original value if a dielectric slab of thickness $t=d / 2$ is inserted between the plates (d is the separation between the plates). The dielectric constant of the slab is
(A) 8
(B) 4
(C) 6
(D) 2

Vysakh M
Vysakh M
Numerade Educator
02:16

Problem 1617

The plates of a parallel capacitor are charged up to $100 \mathrm{~V}$. If $2 \mathrm{~mm}$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6 \mathrm{~mm}$ the dielectric constant of the plate is
(A) 5
(B) 4
(C) $1.25$
(D) $2.5$

Vysakh M
Vysakh M
Numerade Educator
01:02

Problem 1618

A parallel plate air capacitor has a capacitance $18 \mu \mathrm{F}$. If the distance between the plates is tripled and a dielectric medium is introduced, the capacitance becomes $72 \mu \mathrm{F}$. The dielectric constant of the medium is
(A) 4
(B) 12
(C) 9
(D) 2

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 1619

Iaking earth to be a metallic spheres, its capacity will approximately be
(A) $6.4 \times 10^{6} \mathrm{~F}$
(B) $700 \mathrm{pF}$
(C) $711 \mu \mathrm{F}$
(D) $700 \mathrm{pF}$

Narayan Hari
Narayan Hari
Numerade Educator
02:42

Problem 1620

A parallel plate capacitor has the space between its plates filled by two slabs of thickness $(\mathrm{d} / 2)$ each and dielectric constant $\mathrm{K}_{1}$ and $\mathrm{K}_{2}$ If $\mathrm{d}$ is the plate separation of the capacitor, then capacity of the capacitor is ..........
(A) $\left[\left(2 \mathrm{~d} \in_{0}\right) / \mathrm{A}\right]\left[\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right) /\left(\mathrm{K}_{1} \mathrm{~K}_{2}\right)\right]$
(B) $\left[\left(2 \mathrm{~A} \in_{0}\right) / \mathrm{d}\right]\left[\left(\mathrm{K}_{1} \mathrm{~K}_{2}\right) /\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right)\right]$
(C) $\left[\left(2 \mathrm{Ad} \epsilon_{0}\right) / \mathrm{d}\right]\left[\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right) /\left(\mathrm{K}_{1} \mathrm{~K}_{2}\right)\right]$
d] $\left(K_{1}+K_{2}\right)$
(D) $\left[\left(2 \mathrm{~A} \in_{0}\right) /\right.$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:30

Problem 1621

For the circuit shown in figure the charge on $4 \mu \mathrm{F}$ capacitor is
(A) $20 \mu \mathrm{c}$
(B) $24 \mu \mathrm{c}$
(C) $30 \mu \mathrm{c}$
(D) $54 \mu \mathrm{c}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:13

Problem 1622

The capacitors of capacitance $4 \mu \mathrm{F}, 6 \mu \mathrm{F}$ and $12 \mu \mathrm{F}$ are connected first in series and then in parallel. What is the ratio of equivalent capacitance in the two cases?
(A) $2: 3$
(B) $11: 1$
(C) $1: 11$
(D) $1: 3$

Narayan Hari
Narayan Hari
Numerade Educator
01:18

Problem 1623

Large number of capacitors of rating $10 \mu \mathrm{F} / 200 \mathrm{~V} \mathrm{~V}$ are available. The minimum number of capacitors required to design a $10 \mu \mathrm{F} / 700 \mathrm{~V}$ capacitor is
(A) 16
(B) 8
(C) 4
(D) 7

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 1624

A variable condenser is permanently connected to a $100 \mathrm{~V}$ battery. If capacitor is changed from $2 \mu \mathrm{F}$ to $10 \mu \mathrm{F}$. then energy changes is equal to
(A) $2 \times 10^{-2} \mathrm{~J}$
(B) $2.5 \times 10^{-2} \mathrm{~J}$
(C) $6.5 \times 10^{-2} \mathrm{~J}$
(D) $4 \times 10^{-2} \mathrm{~J}$

Narayan Hari
Narayan Hari
Numerade Educator
01:31

Problem 1625

Two positive point charges of $12 \mu \mathrm{c}$ and $8 \mu \mathrm{c}$ are placed $10 \mathrm{~cm}$ apart in air. The work done to bring them $4 \mathrm{~cm}$ closer is
(A) Zero
(B) $4.8 \mathrm{~J}$
(C) $3.5 \mathrm{~J}$
(D) $-5.8 \mathrm{~J}$

Narayan Hari
Narayan Hari
Numerade Educator
04:04

Problem 1626

1000 similar electrified rain drops merge together into one drop so that their total charge remains unchanged. How is the electric energy affected?
(A) 100 times
(B) 200 times
(C) 400 times
(D) 102 times

Vysakh M
Vysakh M
Numerade Educator
03:47

Problem 1627

There are 10 condensers each of capacity $5 \mu \mathrm{F}$. The ratio between maximum and minimum capacities obtained from these condensers will be
(A) $40: 1$
(B) $25: 5$
(C) $60: 3$
(D) $100: 1$

Vysakh M
Vysakh M
Numerade Educator
04:02

Problem 1628

A parallel plate capacitor is made by stocking $\mathrm{n}$ equally spaced plates connected alternately. If the capacitance between any two plates is $\mathrm{x}$, then the total capacitance is,
(A) $\mathrm{nx}$
(B) $n x^{2}$
(C) $(\mathrm{n} / \mathrm{x})$
(D) $(\mathrm{n}-1) \mathrm{x}$

Vysakh M
Vysakh M
Numerade Educator
01:29

Problem 1629

For the circuit shown figure, which of the following statements is true ?
(A) With $\mathrm{S}_{1}$ closed $\mathrm{V}_{1}=15 \mathrm{~V}, \mathrm{~V}_{2}=20 \mathrm{~V}$
(B) With $\mathrm{S}_{3}$ closed $\mathrm{V}_{1}=\mathrm{V}_{2}=20 \mathrm{~V}$
(C) With $\mathrm{S}_{1}$ and $\mathrm{S}_{3}$ closed $\mathrm{V}_{1}=\mathrm{V}_{2}=0$
(D) With $\mathrm{S}_{1}$ and $\mathrm{S}_{3}$ closed $\mathrm{V}_{1}=30 \mathrm{~V}, \mathrm{~V}_{2}=20 \mathrm{~V}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:03

Problem 1630

Two identical metal plates are given positive charges $\mathrm{Q}_{1}$ and $\mathrm{Q}_{2}\left(<\mathrm{Q}_{1}\right)$ respectively. If they are now brought close to gather to form a parallel plate capacitor with capacitance $\mathrm{c}$, the potential difference between them is
(A) $\left[\left(Q_{1}+Q_{2}\right) /(2 c)\right]$
(B) $\left[\left(\mathrm{Q}_{1}+\mathrm{Q}_{2}\right) / \mathrm{c}\right]$
(C) $\left[\left(\mathrm{Q}_{1}-\mathrm{Q}_{2}\right) /(2 \mathrm{c})\right]$
(D) $\left[\left(\mathrm{Q}_{1}-\mathrm{Q}_{2}\right) / \mathrm{c}\right]$

Narayan Hari
Narayan Hari
Numerade Educator
01:51

Problem 1631

Two identical metal plates are given positive charges $\mathrm{Q}_{1}$ and $\mathrm{Q}_{2}\left(<\mathrm{Q}_{1}\right)$ respectively. If they are now brought close to gather to form a parallel plate capacitor with capacitance $\mathrm{c}$, the potential difference between them is
(A) $\left[\left(Q_{1}+Q_{2}\right) /(2 c)\right]$
(B) $\left[\left(\mathrm{Q}_{1}+\mathrm{Q}_{2}\right) / \mathrm{c}\right]$
(C) $\left[\left(\mathrm{Q}_{1}-\mathrm{Q}_{2}\right) /(2 \mathrm{c})\right]$
(D) $\left[\left(\mathrm{Q}_{1}-\mathrm{Q}_{2}\right) / \mathrm{c}\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:35

Problem 1632

In the arrangement of capacitors shown in figure, each capacitor is of $9 \mu \mathrm{F}$, then the equivalent capacitance between the points $\mathrm{A}$ and $\mathrm{B}$ is
(A) $18 \mu \mathrm{F}$
(B) $9 \mu \mathrm{F}$
(C) $15 \mu \mathrm{F}$
(D) $4.5 \mathrm{Mf}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:02

Problem 1633

The electric potential $\mathrm{V}$ at any point $\mathrm{x}, \mathrm{y}, \mathrm{z}$ (all in meter) in space is given by $\mathrm{V}=4 \mathrm{x}^{2}$ volt. The electric field at the point $(1 \mathrm{~m}, 0,2 \mathrm{~m})$ in $\mathrm{Vm}^{-1}$ is
$(\mathrm{A})+8 \mathrm{i} \wedge$
(B) $-8 \mathrm{i} \wedge$
(C) $-16 \mathrm{i}$
(D) $+16 \mathrm{i}$

Narayan Hari
Narayan Hari
Numerade Educator
01:41

Problem 1634

Two air capacitors $A=1 \mu F, B=4 \mu F$ are connected in series with $35 \mathrm{~V}$ source. When a medium of dielectric constant $\mathrm{K}=3$ is introduced between the plates of $\mathrm{A}$, change on the capacitor changes by
(A) $16 \mu \mathrm{c}$
(B) $32 \mu \mathrm{c}$
(C) $28 \mu \mathrm{c}$
(D) $60 \mu \mathrm{c}$

Narayan Hari
Narayan Hari
Numerade Educator
03:11

Problem 1635

A parallel plate capacitor with air between the plates has a capacitance of $9 \mathrm{pF}$. The separation between its plates is $\mathrm{d}$. The space between the plates is now filled with two dielectrics. One of the dielectric constant $\mathrm{K}_{1}=3$ and thickness $\mathrm{d} / 3$ while the other one has dielectric constant $\mathrm{K}_{2}=6$ and thickness $2 \mathrm{~d} / 3$. Capacitance of the capacitor is
now
(A) $1.8 \mathrm{pF}$
(B) $20.25 \mathrm{pF}$
(C) $40.5 \mathrm{pF}$
(D) $45 \mathrm{pF}$

Vysakh M
Vysakh M
Numerade Educator
01:01

Problem 1636

A thin spherical shell of radius $R$ has charge $Q$ spread uniformly over its surface. Which of the following graphs, figure most closely represents the electric field $\mathrm{E}$ (r) produced by the shell in the range $0 \leq \mathrm{r}<\infty$, where $\mathrm{r}$ is the distance from the centre of the shel1.

Narayan Hari
Narayan Hari
Numerade Educator
01:09

Problem 1637

A parallel plate condenser with dielectric of constant $\mathrm{K}$ between the plates has a capacity $\mathrm{C}$ and is charged to potential $\mathrm{v}$ volt. The dielectric slab is slowly removed from between the plates and reinserted. The net work done by the system in this process is
(A) Zero
(B) $(1 / 2)(\mathrm{K}-1) \mathrm{cv}^{2}$
(C) $(\mathrm{K}-1) \mathrm{cv}^{2}$
(D) $\mathrm{cv}^{2}[(\mathrm{~K}-1) / \mathrm{k}]$

Narayan Hari
Narayan Hari
Numerade Educator
01:02

Problem 1638

Charges are placed on the vertices of a square as shown. Let $E^{\rightarrow}$ be the electric field and $V$ the potential at the centre. If the charges on $\mathrm{A}$ and $\mathrm{B}$ are interchanged with those on $\mathrm{D}$ and $\mathrm{C}$ respectively then
(A) $\mathrm{E}^{-}$ Change $\mathrm{V}$ remains unchanged
(B) $\mathrm{E}^{-}$ remains unchanged, $\mathrm{V}$ changes
(C) Both $\mathrm{E}^{-}$ and $\mathrm{V}$ change
(D) $\mathrm{E}^{-}$ and $\mathrm{V}^{-}$ remain unchanged

Narayan Hari
Narayan Hari
Numerade Educator
01:53

Problem 1639

The potential at a point $\mathrm{x}$ (measured in $\mu \mathrm{m}$ ) due to some charges situated on the $\mathrm{x}$ -axis is given by $\mathrm{V}(\mathrm{x})=\left[(20) /\left(\mathrm{x}^{2}-4\right)\right]$ Volt. The electric field at $\mathrm{x}=4 \mu \mathrm{m}$ is
given by
(A) $(5 / 3) \mathrm{V} \mu \mathrm{m}^{-1}$ and in positive $\mathrm{x}$ - direction
(B) $(10 / 9) \mathrm{V} \mu \mathrm{m}^{-1}$ and in positive $\mathrm{x}$ - direction
(C) $(10 / 9) \mathrm{V} \mu \mathrm{m}^{-1}$ and in positive $\mathrm{x}$ - direction
(D) $(5 / 3) \mathrm{V} \mu \mathrm{m}^{-1}$ and in positive $\mathrm{x}$ - direction

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:02

Problem 1640

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and work done by the battery will be
(A) $(1 / 2)$
(B) $(2 / 1)$
(C) 1
(D) $(1 / 4)$

Narayan Hari
Narayan Hari
Numerade Educator
03:15

Problem 1641

1wo spherical conductors $\mathrm{A}$ and $\mathrm{B}$ of radii $\mathrm{lmm}$ and $2 \mathrm{~mm}$ are separated by a distance of $5 \mathrm{~mm}$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of sphere of $\mathrm{A}$ and $\mathrm{B}$ is
(A) $1: 2$
(B) $2: 1$
(C) $4: 1$
(D) $1: 4$

Vysakh M
Vysakh M
Numerade Educator
01:16

Problem 1642

The following arrangement consists of five identical metal plates marked $1,2,3,4$ and 5 parallel to each other. Area of each plate is $\mathrm{A}$ and separation between the successive plates is $\mathrm{d}$. The capacitance between $\mathrm{P}$ and $\mathrm{Q}$ is
(A) $5\left[\left(\mathrm{~A} \in_{0}\right) / \mathrm{d}\right]$
(B) (7/3) $\left[\left(\mathrm{A} \in_{0}\right) / \mathrm{d}\right]$
(C) $(5 / 3)\left[\left(\mathrm{A} \in_{0}\right) / \mathrm{d}\right]$
(D) $(4 / 3)\left[\left(\mathrm{A} \in_{0}\right) / \mathrm{d}\right]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:52

Problem 1643

A parallel plate capacitor of capacitance $5 \mu \mathrm{F}$ and plate separation $6 \mathrm{~cm}$ is connected to a $1 \mathrm{~V}$ battery and charged. A dielectric of dielectric constant 4 and thickness $4 \mathrm{~cm}$ is introduced between the plates of the capacitor. The additional charge that flows into the capacitor from the battery is
(A) $2 \mu \mathrm{c}$
(B) $5 \mu \mathrm{c}$
(C) $3 \mu \mathrm{c}$
(D) $10 \mu \mathrm{c}$

Vysakh M
Vysakh M
Numerade Educator
02:54

Problem 1644

For circuit the equivalent capacitance between points $\mathrm{P}$ and $\mathrm{Q}$ is if $\mathrm{C}_{1}=2 \mu \mathrm{F}, \mathrm{C}_{2}=3 \mu \mathrm{F}, \mathrm{C}_{3}=5 \mu \mathrm{F}, \mathrm{C}_{4}=10 \mu \mathrm{F}$.
(A) $6 \mu \mathrm{F}$
(B) $4 \mu \mathrm{F}$
(C) $(3 / 2) \mu \mathrm{F}$
(D) $5 \mu \mathrm{F}$

Vysakh M
Vysakh M
Numerade Educator
01:10

Problem 1645

Four identical capacitors are connected in series with a $10 \mathrm{~V}$ battery as shown in the figure. Potentials at $\mathrm{A}$ and $\mathrm{B}$ are
(A) $10 \mathrm{~V}, 0 \mathrm{~V}$
(B) $5 \mathrm{~V},-5 \mathrm{~V}$
(C) $7.5 \mathrm{~V},-2.5 \mathrm{~V}$
(D) $7.5 \mathrm{~V}, 2.5 \mathrm{~V}$

Narayan Hari
Narayan Hari
Numerade Educator
04:56

Problem 1646

64 identical drops of mercury are charged simultaneously to the same potential of 10 volt. Assuming the drops to be spherical, if all the charged drops are made to combine to form one large drop, then its potential will be
(A) $100 \mathrm{~V}$
(B) $320 \mathrm{~V}$
(C) $640 \mathrm{~V}$
(D) $160 \mathrm{~V}$

Vysakh M
Vysakh M
Numerade Educator
01:02

Problem 1647

Two metal plate form a parallel plate capacitor. The distance between the plates is $\mathrm{d}$. A metal sheet of thickness $\mathrm{d} / 2$ and of the same area is introduced between the plates. What is the ratio of the capacitance in the two cases?
(A) $4: 1$
(B) $3: 1$
(C) $2: 1$
(D) $5: 1$

Narayan Hari
Narayan Hari
Numerade Educator
04:13

Problem 1648

The circular plates $\mathrm{A}$ and $\mathrm{B}$ of a parallel plate air capacitor have a diameter of $0.1 \mathrm{~m}$ and are $2 \times 10^{-3} \mathrm{~m}$ apart. The plates $\mathrm{C}$ and $\mathrm{D}$ of a similar capacitor have a diameter of $0.1 \mathrm{~m}$ and are $3 \times 10^{-3} \mathrm{~m}$ apart. Plate $\mathrm{A}$ is earthed. Plates $\mathrm{B}$ and $\mathrm{D}$ are connected together. Plate $\mathrm{C}$ is connected to the positive pole of a $120 \mathrm{~V}$ battery whose negative is earthed, The energy stored in the system is
(A) $0.1224 \mu \mathrm{J}$
(B) $0.2224 \mu \mathrm{J}$
(C) $0.4224 \mu \mathrm{J}$
(D) $0.3224 \mu \mathrm{J}$

Vysakh M
Vysakh M
Numerade Educator
01:12

Problem 1649

Two parallel conducting plates of area $\mathrm{A}=2.5 \mathrm{~m}^{2}$ each are placed $6 \mathrm{~mm}$ apart and are both earthed. A third plate, identical with the first two, is placed at a distance of $2 \mathrm{~mm}$ from one of the earthed plates and is given a charged of $1 \mathrm{C}$. The potential of the central plate is
(A) $6 \times 10^{7} \mathrm{~V}$
(B) $3 \times 10^{7} \mathrm{~V}$
(C) $2 \times 10^{7} \mathrm{~V}$
(D) $4 \times 10^{7} \mathrm{~V}$

Narayan Hari
Narayan Hari
Numerade Educator
01:53

Problem 1650

Calculate energy stored in the network where network of five capacitor is connected to $100 \mathrm{v}$ supply.
(A)Zero
(B) $4 \mathrm{~J}$
(C) $0.02 \mathrm{~J}$
(D) $1.85 \mathrm{~J}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:53

Problem 1651

Two identical capacitors 1 and 2 are connected in series to a battery as shown in figure. Capacitor 2 contains a dielectric slab of constant $\mathrm{K} . \mathrm{Q}_{1}$ and $\mathrm{Q}_{2}$ are the charges stored in 1 and 2 . Now, the dielectric slab is removed and the corresponding charges are $Q_{1}^{\prime}$ and $Q_{2}^{\prime} 2$. Then
(A) $\left(\mathrm{Q}_{1}^{1} / \mathrm{Q}_{1}^{1}\right)[(\mathrm{K}+1) / \mathrm{K}]$
(B) $\left(\mathrm{Q}_{1}^{1} / \mathrm{Q}_{1}^{1}\right)(\mathrm{K} / 2)$
(C) $\left(\mathrm{Q}_{2}{ }^{1} / \mathrm{Q}_{2}\right)[(\mathrm{K}+1) /(2 \mathrm{~K})]$
(D) $\left(\mathrm{Q}_{2}{ }^{1} / \mathrm{Q}_{2}\right)[(\mathrm{K}+1) / \mathrm{K}]$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:14

Problem 1652

A parallel plate capacitor has plate of area $\mathrm{A}$ and separation
d. It is charged to a potential difference $\mathrm{V}_{0}$. The charging battery is disconnected and the plates are pulled apart to three times the initial separation. The work required to separate the plates is
(A) $\left[\left(\mathrm{A} \in_{0} \mathrm{~V}_{0}^{2}\right) / \mathrm{d}\right]$
(B) $\left[\left(\mathrm{A} \in{ }_{0} \mathrm{~V}_{0}^{2}\right) /(2 \mathrm{~d})\right]$
(C) $\left[\left(\mathrm{A} \in{ }_{0} \mathrm{~V}_{0}{ }^{2}\right) /(3 \mathrm{~d})\right]$
(D) $\left[\left(\mathrm{A} \in{ }_{0} \mathrm{~V}_{0}{ }^{2}\right) /(4 \mathrm{~d})\right]$

Vysakh M
Vysakh M
Numerade Educator
01:03

Problem 1653

Two identical capacitors have the same capacitance $\mathrm{C}$. one of them is charged to a potential $\mathrm{V}_{1}$ and the other to $\mathrm{V}_{2}$. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is
(A) $(1 / 4) \mathrm{C}\left(\mathrm{V}_{1}^{2}-\mathrm{V}_{2}^{2}\right)$
(B) $(1 / 4) \mathrm{C}\left(\mathrm{V}_{1}^{2}+\mathrm{V}_{2}^{2}\right)$
(C) $(1 / 4) \mathrm{C}\left(\mathrm{V}_{1}-\mathrm{V}_{2}\right)^{2}$
(D) $(1 / 4) \mathrm{C}\left(\mathrm{V}_{1}+\mathrm{V}_{2}\right)^{2}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:39

Problem 1654

A parallel plate air capacitor has a capacitance $\mathrm{C}$. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be
(A) $200 \%$
(B) $33.3 \%$
(C) $400 \%$
(D) $66.6 \%$

Vysakh M
Vysakh M
Numerade Educator
02:16

Problem 1655

A network of six identical capacitors, each of value $\mathrm{C}$ is made as shown in figure. Equivalent capacitance between points $\mathrm{A}$ and $\mathrm{B}$ is
(A) (C / 4)
(B) (3C / 4)
(C) (4C / 3)
(D) $3 \mathrm{C}$

Vysakh M
Vysakh M
Numerade Educator
02:56

Problem 1658

An electric circuit requires a total capacitance of $2 \mu \mathrm{F}$ across a potential of $1000 \mathrm{~V}$. Large number of $1 \mu \mathrm{F}$ capacitances are available each of which would breakdown if the potential is more then $350 \mathrm{~V}$. How many capacitances are required to make the circuit?
(A) 24
(B) 12
(C) 20
(D) 18

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:04

Problem 1659

Read the assertion and reason carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Assertion: The coulomb force is the dominating force in the universe. Reason: The coulomb force is weaker than the gravitational force.

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 1660

Read the assertion and reason carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Assertion: If three capacitors of capacitance $\mathrm{C}_{1}<\mathrm{C}_{2}<\mathrm{C}_{3}$ are connected in parallel then their equivalent capacitance $\mathrm{C}_{\mathrm{p}}>\mathrm{C}_{3}$
Reason: $\left(1 / C_{p}\right)=\left(1 / C_{1}\right)+\left(1 / C_{2}\right)+\left(1 / C_{3}\right)$

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 1661

Read the assertion and reason carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Assertion: A metallic shield in form of a hollow shell may be built to block an electric field. Reason: In a hollow spherical shield, the electric field inside it is zero at every point.

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 1662

Read the assertion and reason carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Assertion: Electrons move away from a low potential to high potential region. Reason: Because electrons have negative charge

Narayan Hari
Narayan Hari
Numerade Educator
01:02

Problem 1663

Read the assertion and reason carefully to mark the correct option out of the options given below :
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Assertion: If the distance between parallel plates of a capacitor is halved and dielectric constant is made three times, then the capacitance becomes 6 times. Reason: Capacity of the capacitor does not depend upon the nature of the material.

Narayan Hari
Narayan Hari
Numerade Educator
02:46

Problem 1664

Read the assertion and reason carefully to mark the correct option out of the options given below :
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Assertion: A parallel plate capacitor is connected across battery through a key. A dielectric slab of constant $\mathrm{K}$ is introduced between the plates. The energy which is stored becomes $\mathrm{K}$ times. Reason: The surface density of charge on the plate remains constant or unchanged.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:01

Problem 1665

Read the assertion and reason carefully to mark the correct option out of the options given below :
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Assertion: Electric lines of force cross each other. Reason: Electric field at a point superimpose to give one resultant electric field.

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 1666

Read the assertion and reason carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Assertion: If a proton and an electron are placed in the same uniform electric field. They experience different acceleration. Reason: Electric force on a test charge is independent of its mass.

Narayan Hari
Narayan Hari
Numerade Educator
01:02

Problem 1667

Read the assertion and reason carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Assertion: Dielectric breakdown occurs under the influence of an intense light beam. Reason: Electromagnetic radiations exert pressure.

Narayan Hari
Narayan Hari
Numerade Educator
01:01

Problem 1668

Kead the assertion and reason carefully to mark the correct option out of the options given below :
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.
Assertion: When charges are shared between any two bodies, no charge is really lost, but some loss of energy does occur. Reason: Some energy disappears in the form of heat, sparking etc.

Narayan Hari
Narayan Hari
Numerade Educator