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A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar

Chapter 16

Electromagnetic Induction - all with Video Answers

Educators

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Chapter Questions

01:38

Problem 1

A uniform but time varying magnetic field exists in cylindrical region and directed into the paper. If field decreases with time and a positive charge placed at any point inside the region, then it moves
(A) along 1
(B) along 2
(C) along 3
(D) along 4

Ankur S
Ankur S
Numerade Educator
02:01

Problem 2

Two circular coils $P$ and $Q$ are arranged coaxially as shown, and the sign convention adopted that currents are taken as positive when flow in the direction of the arrows
(A) If $P$ carries a steady positive current and $P$ is moved towards $Q$, a positive current is induced in $Q$.
(B) If $P$ carries a steady positive current and $Q$ is moved towards $P$, a negative current is induced in $Q$.
(C) If a positive current flowing in $P$ is switched off, a negative current is induced momentarily in $Q$.
(D) If both coils carry positive currents, the coils repel one another.

Ankur S
Ankur S
Numerade Educator
01:05

Problem 3

Two coils of self-inductance $4 \mathrm{H}$ and $16 \mathrm{H}$ are wound on the same iron core. The coefficient of mutual inductance for them will be
(A) $8 \mathrm{H}$
(B) $10 \mathrm{H}$
(C) $20 \mathrm{H}$
(D) $64 \mathrm{H}$

Ankur S
Ankur S
Numerade Educator
01:09

Problem 4

Two pure inductors, each of self-inductance $L$ are connected in parallel but are well separated from each other, then the total inductance is
(A) $L$
(B) $2 L$
(C) $L / 2$
(D) $L / 4$

Ankur S
Ankur S
Numerade Educator
01:34

Problem 5

SI unit of inductance can be written as
(A) Weber/Ampere
(B) Joule/Ampere $^{2}$
(C) Ohm/Second
(D) All of the above

Ankur S
Ankur S
Numerade Educator
01:17

Problem 6

There is a current of $1.344 \mathrm{~A}$ in a copper wire whose area of cross-section normal to the length of the wire is $1 \mathrm{~mm}^{2}$. If the number of free electrons per $\mathrm{cm}^{3}$ is $8.4 \times 10^{22}$, then the drift velocity of electrons will be
(A) $1.0 \mathrm{~mm} \mathrm{~s}$
(B) $1.0$ meter s
(C) $0.1 \mathrm{~mm} \mathrm{~s}$
(D) $0.01 \mathrm{~mm} \mathrm{~s}$

Ankur S
Ankur S
Numerade Educator
02:11

Problem 7

Two straight long conductors $A O B$ and $C O D$ are perpendicular to each other and carry currents $I_{1}$ and $I_{2}$, respectively. The magnitude of the magnetic induction at a point $P$ at a distance $a$ from the point $O$ in a direction perpendicular to the plane $A B C D$ is
(A) $\frac{\mu_{0}}{2 \pi a}\left(I_{1}+I_{2}\right)$
(B) $\frac{\mu_{0}}{2 \pi a}\left(I_{1}-I_{2}\right)$
(C) $\frac{\mu_{0}}{2 \pi a}\left(I_{1}^{2}+I_{2}^{2}\right)^{1 / 2}$
(D) $\frac{\mu_{0}}{2 \pi a}\left(\frac{I_{1} I_{2}}{I_{1}+I_{2}}\right)$

Ankur S
Ankur S
Numerade Educator
01:18

Problem 8

A bar magnet, of magnetic moment $M$, is placed in a magnetic field of induction $B$. The torque exerted on it is
(A) $\vec{M} \cdot \vec{B}$
(B) $\vec{B} \times \vec{M}$
(C) $\vec{M} \times \vec{B}$
(D) $-\vec{B} \cdot \vec{M}$

Ankur S
Ankur S
Numerade Educator
01:05

Problem 9

In a coil when current changes from $10 \mathrm{~A}$ to $2 \mathrm{~A}$ in time $0.1 \mathrm{~s}$, induced EMF is $3.20 \mathrm{~V}$. The self-inductance of coil is
(A) $4 \mathrm{H}$
(B) $0.4 \mathrm{H}$
(C) $0.04 \mathrm{H}$
(D) $5 \mathrm{H}$

Ankur S
Ankur S
Numerade Educator
01:08

Problem 10

A choke coil has
(A) high inductance and high resistance.
(B) low inductance and low resistance.
(C) high inductance and low resistance.
(D) low inductance and high resistance.

Ankur S
Ankur S
Numerade Educator
01:13

Problem 11

The EMF induced in a 1 millihenry inductor in which the current changes from $5 \mathrm{~A}$ to $3 \mathrm{~A}$ in $10^{-3}$ second is
(A) $2 \times 10^{-6} \mathrm{~V}$
(B) $8 \times 10^{-6} \mathrm{~V}$
(C) $2 \mathrm{~V}$
(D) $8 \mathrm{~V}$

Ankur S
Ankur S
Numerade Educator
01:24

Problem 12

A conducting square loop of side $L$ and resistance $R$ moves in its plane with a uniform velocity $v$ perpendicular to one of its sides. A magnetic field $B$, constant in space and time, pointing perpendicular and into the plane of the loop exists everywhere as shown in Fig. 16.38. The current induced in the loop is
(A) $B L v / R$ clockwise
(B) $B L v / R$ anti-clockwise
(C) $2 B L v / R$ anti-clockwise
(D) Zero

Ankur S
Ankur S
Numerade Educator
01:01

Problem 13

A magnetic needle is kept in a non-uniform magnetic field. It experiences
(A) A force and torque
(B) A force but not a torque
(C) A torque but not a force
(D) Neither a force nor a torque

Narayan Hari
Narayan Hari
Numerade Educator
01:27

Problem 14

A current $i$ ampere flows along an infinitely long straight thin-walled tube, then the magnetic induction at any point inside the tube at a distance $r$ from centre is
(A) Infinite
(B) Zero
(C) $\frac{\mu_{0}}{4 \pi} \cdot \frac{2 i}{r}$
(D) $\frac{2 i}{r}$

Ankur S
Ankur S
Numerade Educator
01:12

Problem 15

A proton and an alpha particle enter a uniform magnetic field with the same velocity. The period of rotation of the alpha particle will be
(A) four times that of the proton.
(B) two times that of the proton.
(C) three times that of the proton.
(D) same as that of the proton.

Ankur S
Ankur S
Numerade Educator
01:17

Problem 16

A coil having an area $A_{0}$ is placed in a magnetic field which changes from $B_{0}$ to $4 B_{0}$ in time interval $t$. The average EMF induced in the coil will be
(A) $\frac{3 A_{0} B_{0}}{t}$
(B) $\frac{4 A_{0} B_{0}}{t}$
(C) $\frac{3 B_{0}}{A_{0} t}$
(D) $\frac{4 B_{0}}{A_{0} t}$

Ankur S
Ankur S
Numerade Educator
01:13

Problem 17

When the current changes from $+2 \mathrm{~A}$ to $-2 \mathrm{~A}$ in $0.05 \mathrm{~s}$, an EMF of $8 \mathrm{~V}$ is induced in a coil. The coefficient of self-induction of the coil is
(A) $0.1 \mathrm{H}$
(B) $0.2 \mathrm{H}$
(C) $0.4 \mathrm{H}$
(D) $0.8 \mathrm{H}$

Ajay Singhal
Ajay Singhal
Numerade Educator
01:19

Problem 18

A circular loop of radius $R=20 \mathrm{~cm}$ is placed in a uniform magnetic field $\vec{B}=2 \mathrm{~T}$ in $x-y$ plane as shown in Fig. 16.39. The loop carries a current $i=1.0 \mathrm{~A}$ in the direction shown in the Fig. 16.39. Find the magnitude of torque acting on the loop.
(A) $0.16 \pi \mathrm{N} / \mathrm{m}$.
(B) $0.08 \pi \mathrm{N} / \mathrm{m}$.
(C) $\frac{0.08}{\sqrt{2}} \pi \mathrm{N} / \mathrm{m}$.
(D) $\frac{0.16}{\sqrt{2}} \pi \mathrm{N} / \mathrm{m}$.

Ankur S
Ankur S
Numerade Educator
01:09

Problem 19

An average EMF of $20 \mathrm{~V}$ is induced in an inductor when the current in it changed from $2.5 \mathrm{~A}$ in one direction to the same value in opposite direction in $0.1 \mathrm{~s}$, the self-inductance of inductor is
(A) $0.4 \mathrm{H}$
(B) $1 \mathrm{H}$
(C) $2 \mathrm{H}$
(D) $0.6 \mathrm{H}$

Ankur S
Ankur S
Numerade Educator
01:43

Problem 20

A conducting rod of length $2 \ell$ is rotating with constant angular speed $\omega$ about its perpendicular bisector. A uniform magnetic field $\vec{B}$ exists parallel to the axis of rotation. The EMF induced between two ends of the rod is
(A) $B \omega \ell^{2}$
(B) $\frac{1}{2} B \omega \ell^{2}$
(C) $\frac{1}{8} B \omega \ell^{2}$
(D) Zero

Ankur S
Ankur S
Numerade Educator
01:07

Problem 21

A $50 \mathrm{mH}$ coil carries a current of $2 \mathrm{~A}$, the energy stored in it in $\mathrm{J}$ is
(A) $0.05$
(B) $0.1$
(C) $0.5$
(D) 1

Ankur S
Ankur S
Numerade Educator
01:18

Problem 22

A capacitance $C$ is connected to a conducting rod of length $\ell$ moving with a velocity $v$ in a transverse magnetic field $B$ then the charge developed in the capacitor is
(A) Zero
(B) $B \ell v C$
(C) $\frac{B l v C}{2}$
(D) $\frac{B l v C}{3}$

Ankur S
Ankur S
Numerade Educator
01:40

Problem 23

A particle of mass $M$ and charge $Q$ moving with a velocity $\vec{v}$ describes a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B$. The work done by the field when the particle completes a full circle is
(A) Zero
(B) $B Q 2 \pi R$
(C) $B Q v(2 \pi R)$
(D) $\left(\frac{M v^{2}}{R}\right)(2 \pi R)$

Ankur S
Ankur S
Numerade Educator
01:35

Problem 24

A rectangular coil of 100 turns and size $0.1 \mathrm{~m} \times 0.05 \mathrm{~m}$ is placed perpendicular to a magnetic field of $0.1 \mathrm{~T}$.
The induced EMF when the field drops to $0.05 \mathrm{~T}$ is $0.05 \mathrm{~s}$ is
(A) $0.5 \mathrm{~V}$
(B) $1.0 \mathrm{~V}$
(C) $1.5 \mathrm{~V}$
(D) $2.0 \mathrm{~V}$

Ankur S
Ankur S
Numerade Educator
01:08

Problem 25

If a coil of metal wire is kept stationary in a non-uniform magnetic field,
(A) An EMF and current are both induced in the coil
(B) A current but no EMF is induced in the coil
(C) An EMF but no current is induced in the coil
(D) Neither EMF nor current is induced in the coil

Ankur S
Ankur S
Numerade Educator
01:05

Problem 26

A flat coil carrying a current has a magnetic moment $\vec{\mu}$. It is placed in a magnetic field $\vec{B}$. The torque on the coil is $\vec{\tau}$, then
(A) $\vec{\tau}=\vec{\mu} \cdot \vec{B}$
(B) $\vec{\tau}=\vec{B} \times \vec{\mu}$
(C) $|\vec{\tau}|=\vec{\mu} \cdot \vec{B}$
(D) $\vec{\tau}$ is perpendicular to both $\vec{\mu}$ and $\vec{B}$.

Ankur S
Ankur S
Numerade Educator
01:35

Problem 27

The torque acting on this loop will be
(A) Zero
(B) $\frac{I a^{2} B_{0}}{2}$
(C) $\frac{2 I a^{2} B_{0}}{3}$
(D) None

Ankur S
Ankur S
Numerade Educator
01:19

Problem 28

A conducting loop carrying a current $I$ is placed in a uniform magnetic field pointing into the plane as shown in Fig. 16.40. The loop will have tendency to Fig. $16.40$
(A) Contract
(B) Expand
(C) Move towards positive $x$-axis
(D) Move towards negative $x$-axis

Ankur S
Ankur S
Numerade Educator
01:35

Problem 29

A rod of length $\ell$ is moved with a velocity $v$ in a magnetic field $B$ as shown in Fig. $16.41$, the equivalent electrical circuit is Fig
(A)
(B)
(C)
(D)

Ankur S
Ankur S
Numerade Educator
02:04

Problem 30

A conducting rod $P Q$ is moving parallel to $x-z$-plane in a uniform magnetic field directed in the positive $y$-direction. The end $P$ of the rod will become
(A) Sometime positive and sometime negative
(B) Positive
(C) Neutral
(D) Negative

Ankur S
Ankur S
Numerade Educator
01:24

Problem 31

What is direction of induced current in the coil as shown in Fig. $16.42$ ? (If rate of increase of current is equal to the rate of decrease.)
(A) Clockwise
(B) Anti-clockwise
(C) $\mathrm{Zero}$
(D) Not defined with same rate

Ankur S
Ankur S
Numerade Educator
01:53

Problem 32

A metallic wire bent into a right $\Delta a b c$ moves with a uniform velocity $v$ as shown in Fig. $16.43, B$ is the strength of uniform magnetic field perpendicular outwards the plane of triangle. The net EMF is ......... and EMF along $a b$ is $\ldots \ldots \ldots$
(A) zero, $B v(b c)$ with $b$ positive
(B) zero, $B v(b c)$ with $a$ positive
(C) $B v(b c)$ with $c$ positive, zero
(D) $B v(b c)$ with $b$ positive, zero

Ankur S
Ankur S
Numerade Educator
01:10

Problem 33

The magnetic flux linked with a coil is $\phi=8 t^{2}+3 t$ $+5 \mathrm{~Wb}$. The induced EMF in the fourth second will be
(A) $145 \mathrm{~V}$
(B) $139 \mathrm{~V}$
(C) $67 \mathrm{~V}$
(D) $16 \mathrm{~V}$

Ankur S
Ankur S
Numerade Educator
01:18

Problem 34

Flux $\phi$ (in weber) in a closed circuit of resistance $10 \Omega$ varies with time $t$ (in seconds) according to the equation $\phi=6 t^{2}-5 t+1$. The magnitude of the induced current in the circuit at $t=0.25 \mathrm{~s}$ is
(A) $0.2 \mathrm{~A}$
(B) $0.6 \mathrm{~A}$
(C) $0.8 \mathrm{~A}$
(D) $1.2 \mathrm{~A}$

Ankur S
Ankur S
Numerade Educator
01:34

Problem 35

A semicircular conducting ring is placed in $y z$-plane in a uniform magnetic field directed along positive $z$-direction. An induced EMF will be developed in the ring if it is moved along.
(A) Positive $x$-direction
(B) Positive $y$-direction
(C) Positive $z$-direction
(D) None of the above

Ankur S
Ankur S
Numerade Educator
01:32

Problem 36

A conducting rod $P Q$ of length $L=1.0 \mathrm{~m}$ is moving with a uniform speed $v=2.0 \mathrm{~m} / \mathrm{s}$ in a uniform magnetic field $B=4.0 \mathrm{~T}$ direction into the paper. A capacitor of capacity $C=10 \mu \mathrm{F}$ is connected as shown in Fig. $16.44$. Then Fig. $16.44$
(A) $q_{A}=+80 \mu \mathrm{C}$ and $q_{B}=-80 \mu \mathrm{C}$.
(B) $q_{A}=-80 \mu \mathrm{C}$ and $q_{B}=+80 \mu \mathrm{C}$.
(C) $q_{A}=0=q_{B}$.
(D) charge stored in the capacitor increases exponentially with time.

Ankur S
Ankur S
Numerade Educator
01:09

Problem 37

The magnetic flux linked with a circuit of resistance 100 ohm increases from 10 to 60 webers. The amount of induced charge that flows in the circuit is (in coulomb)
(A) $0.5$
(B) 5
(C) 50
(D) 100

Ankur S
Ankur S
Numerade Educator
01:26

Problem 38

In an oscillating $L-C$ circuit, the maximum charge on the capacitor is $Q$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is
(A) $\frac{Q}{2}$
(B) $\frac{Q}{\sqrt{2}}$
(C) $\frac{Q}{\sqrt{3}}$
(D) $\frac{Q}{3}$

Ankur S
Ankur S
Numerade Educator
01:12

Problem 39

An equilateral triangular loop having a resistance $R$ and length of each side $\ell$ is placed in a magnetic field which is varying at $\frac{d B}{d t}=1 \mathrm{~T} / \mathrm{S}$. The induced current in the loop will be
(A) $\frac{\sqrt{3}}{4} \frac{l^{2}}{R}$
(B) $\frac{4}{\sqrt{3}} \frac{l^{2}}{R}$
(C) $\frac{\sqrt{3}}{4} \frac{R}{l^{2}}$
(D) $\frac{4}{\sqrt{3}} \frac{R}{l^{2}}$

Ankur S
Ankur S
Numerade Educator
01:32

Problem 40

A metallic square loop $A B C D$ is moving in its own plane with velocity $v$ in a uniform magnetic field perpendicular to its plane as shown in Fig. $16.45 .$ An electric field is induced
(A) In $A D$, but not in $B C$
(B) In $B C$, but not in $A D$
(C) Neither in $A D$ nor in $B C$
(D) In both $A D$ and $B C$

Ankur S
Ankur S
Numerade Educator
01:34

Problem 41

The mutual inductance between two planar concentric rings of radii $r_{1}$ and $r_{2}$ (with $r_{1} \gg r_{2}$ ) placed in air is given by
(A) $\frac{\mu_{0} \pi r_{2}^{2}}{2 r_{1}}$
(B) $\frac{\mu_{0} \pi r_{1}^{2}}{2 r_{2}}$
(C) $\frac{\mu_{0} \pi\left(r_{1}+r_{2}\right)^{2}}{2 r_{1}}$
(D) $\frac{\mu_{0} \pi\left(r_{1}+r_{2}\right)^{2}}{2 r_{2}}$

Ankur S
Ankur S
Numerade Educator
01:34

Problem 42

A coil in the shape of an equilateral triangle of side $\ell$ is suspended between the pole pieces of a permanent magnet such that $\vec{B}$ is in the plane of the coil. If due to a current $i$ in the triangle, a torque $\tau$ acts on it, the side $\ell$ of the triangle is
(A) $\frac{2}{\sqrt{3}}\left(\frac{\tau}{B i}\right)$
(B) $2\left(\frac{\tau}{\sqrt{3} B i}\right)^{1 / 2}$
(C) $\frac{2}{\sqrt{3}}\left(\frac{\tau}{B i}\right)^{1 / 2}$
(D) $\frac{1}{\sqrt{3}}\left(\frac{\tau}{B i}\right)$

Ankur S
Ankur S
Numerade Educator
00:34

Problem 43

When the number of turns in a coil is doubled without any change in the length of the coil, its self-inductance becomes
(A) Four times
(B) Doubled
(C) Halved
(D) Squared

Nidhi Singhi
Nidhi Singhi
Numerade Educator
01:11

Problem 44

A varying magnetic flux linking a coil is given by $\phi=x t^{2}$. If at a time $t=3 \mathrm{~s}$, the EMF induced is $9 \mathrm{~V}$, then the value of $x$ is
(A) $0.66 \mathrm{Wbs}^{-2}$
(B) $1.5 \mathrm{Wbs}^{-2}$
(C) $-0.66 \mathrm{Wbs}^{-2}$
(D) $-1.5 \mathrm{Wbs}^{-2}$

Ankur S
Ankur S
Numerade Educator
01:11

Problem 45

A 100 turns coil shown in Fig. $16.46$ carries a current of $2 \mathrm{~A}$ in a magnetic field $B=0.2 \mathrm{~Wb} / \mathrm{m}^{2}$. The torque acting on the coil isc
(A) $0.32 \mathrm{Nm}$ tending to rotate the side $A D$ out of the page.
(B) $0.32 \mathrm{Nm}$ tending to rotate the side $A D$ into the page.
(C) $0.0032 \mathrm{Nm}$ tending to rotate the side $A D$ out of the page.
(D) $0.0032 \mathrm{Nm}$ tending to rotate the side $A D$ into the page.

Ankur S
Ankur S
Numerade Educator
01:04

Problem 46

The magnetic susceptibility of a material of a rod is 499. Permeability of vacuum is $4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$. Absolute permeability of the material of the rod in henry per meter is
(A) $\pi \times 10^{-4}$
(B) $2 \pi \times 10^{-4}$
(C) $3 \pi \times 10^{-4}$
(D) $4 \pi \times 10^{-4}$

Ankur S
Ankur S
Numerade Educator
01:27

Problem 47

A conducting circular loop is placed in a uniform magnetic field of induction $B$ tesla with its plane normal to the field. Now the radius of the loop starts shrinking at the rate $(d r / d t)$. Then the induced EMF at the instant when the radius is $r$ will be
(A) $\pi r B\left(\frac{d r}{d t}\right)$
(B) $2 \pi r B\left(\frac{d r}{d t}\right)$
(C) $\pi r^{2}\left(\frac{d B}{d t}\right)$
(D) $B \frac{\pi r^{2}}{2} \frac{d r}{d t}$

Ankur S
Ankur S
Numerade Educator
01:57

Problem 48

If the flux of magnetic induction through a coil of resistance $R$ and having $n$ turns changes from $\phi_{1}$ to $\phi_{2}$, then the magnitude of the charge that passes through the coil is
(A) $\frac{\left(\phi_{2}-\phi_{1}\right)}{R}$
(B) $\frac{n\left(\phi_{2}-\phi_{1}\right)}{R}$
(C) $\frac{\left(\phi_{2}-\phi_{1}\right)}{n R}$
(D) $\frac{n R}{\left(\phi_{2}-\phi_{1}\right)}$

Ankur S
Ankur S
Numerade Educator
01:09

Problem 49

A varying magnetic flux linking a coil is given by $\phi=3 t^{2}$. The magnitude of induced EMF in the loop at $t=3 \mathrm{~s}$ is
(A) $3 \mathrm{~V}$
(B) $9 \mathrm{~V}$
(C) $18 \mathrm{~V}$
(D) $27 \mathrm{~V}$

Ankur S
Ankur S
Numerade Educator
01:32

Problem 50

A horizontal telegraph wire $0.5 \mathrm{~km}$ long running east and west is a part of a circuit whose resistance is $2.5 \Omega$. The wire falls to the ground from a height of $5 \mathrm{~m}$. If $g=10.0 \mathrm{~m} / \mathrm{s}^{2}$ and horizontal component of earth's magnetic field is $2 \times 10^{-5}$ weber $/ \mathrm{m}^{2}$, then the current induced in the circuit just before the wire hits the ground will be
(A) $0.7 \mathrm{~A}$
(B) $0.04 \mathrm{~A}$
(C) $0.02 \mathrm{~A}$
(D) $0.01 \mathrm{~A}$

Ankur S
Ankur S
Numerade Educator
01:59

Problem 51

A coil of $20 \times 20 \mathrm{~cm}$ having 30 turns is making $30 \mathrm{rps}$ in a magnetic field of 1 tesla. The peak value of the induced EMF is approximately
(A) $452 \mathrm{~V}$
(B) $226 \mathrm{~V}$
(C) $113 \mathrm{~V}$
(D) $339 \mathrm{~V}$

Ankur S
Ankur S
Numerade Educator
02:07

Problem 52

Two particles each of mass $m$ and charge $q$ are attached to the two ends of a light rigid rod of length $2 \ell$. The rod is rotated at a constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is
(A) $\frac{q}{2 m} \quad$ (B) $\frac{q}{m}$
(C) $\frac{2 q}{m}$
(D) $\frac{q}{\pi m}$

Ankur S
Ankur S
Numerade Educator
10:12

Problem 53

Loop $A$ of radius $r(r \ll R)$ moves towards a constant current carrying loop $B$ with a constant velocity $v$ in such a way that their planes are parallel and coaxial. The distance between the loops when the induced EMF in loop $A$ is maximum is
(A) $R$
(B) $\frac{R}{\sqrt{2}}$
(C) $\frac{R}{2}$
(D) $R\left(1-\frac{1}{\sqrt{2}}\right)$

Ravindra Yadav
Ravindra Yadav
Numerade Educator
01:28

Problem 54

A uniform current carrying ring of mass $m$ and radius $R$ is connected by a massless string as shown in Fig. 16.47. A uniform magnetic field $B_{0}$ exists in the region to keep the ring in horizontal position, then the current in the ring is ( $\ell=$ length of string)
(A) $\frac{m g}{\pi R B_{0}}$
(B) $\frac{m g}{R B_{0}}$
(C) $\frac{m g}{3 \pi R B_{0}}$
(D) $\frac{m g l}{\pi R^{2} B_{0}}$

Ankur S
Ankur S
Numerade Educator
02:02

Problem 55

A conducting rod $A B$ moves parallel to $x$-axis in the $x-y$ plane. A uniform magnetic field $B$ pointing normally out of the plane exists throughout the region. A force $F$ acts perpendicular to the rod, so that the rod moves with uniform velocity $v$. The force $F$ is given by (neglect resistance of all the wires).
(A) $\frac{v B^{2} l^{2}}{R} e^{-t / R C}$
(B) $\frac{v B^{2} l^{2}}{R}$
(C) $\frac{v B^{2} l^{2}}{R}\left(1-e^{-t / R C}\right)$
(D) $\frac{v B^{2} l^{2}}{R}\left(1-e^{-2 t / R C}\right)$

Ankur S
Ankur S
Numerade Educator
01:48

Problem 56

A conducting rod of mass $m$ and length $\ell$ is connected by two identical springs as shown in Fig. $16.48$. Initially, the system is in equilibrium. A uniform magnetic field of magnitude $B$ directed perpendicular to the plane of the paper outwards also exists in the region. If a current $I$ is switched on, it passes from $P$ to $Q$ through the rod. Further maximum elongation in the spring is [Given: $|m g|=|B I \ell|$ \}
(A) $\frac{B I 1}{K}$
(B) $\frac{B I 1}{4 K}$
(C) $\frac{B I l}{8 K}$
(D) $\frac{B I 1}{16 K}$

Hunza Gilgit
Hunza Gilgit
Numerade Educator
02:07

Problem 57

A uniform but time varying magnetic field is present in a circular region of radius $R$. The magnetic field is perpendicular and into the plane of the paper and the magnitude of the field is increasing at a constant rate $\alpha$. There is a straight conducing rod of length $2 R$ placed as shown in Fig. 16.49. The magnitude of induced EMF across the rod is
(A) $\pi R^{2} \alpha$
(B) $\frac{\pi R^{2} \alpha}{2}$
(C) $\frac{R^{2} \alpha}{\sqrt{2}}$
(D) $\frac{\pi R^{2} \alpha}{4}$

Ankur S
Ankur S
Numerade Educator
01:15

Problem 58

The diagram shows a solenoid carrying time varying current $I=I_{0} t$. On the axis of this solenoid, a ring has been placed. The mutual inductance of the ring and the solenoid is $M$ and the self-inductance of the ring is $L$. If the resistance of the ring is $R$ then maximum current which can flow through the ring is
(A) $\frac{(2 M+L) I_{0}}{R}$
(B) $\frac{M I_{0}}{R}$
(C) $\frac{(2 M-L) I_{0}}{R}$
(D) $\frac{(M+L) I_{0}}{R}$

Ankur S
Ankur S
Numerade Educator
01:15

Problem 59

A metallic ring of radius $R$ moves in a vertical plane in the presence of a uniform magnetic field $B$ perpendicular to the plane of the ring. At any given instant of time, its centre of mass moves with a velocity $v$ while ring rotates in its COM frame with angular velocity $\omega$ as shown in Fig. $16.50 .$ The magnitude of induced EMF between points $O$ and $P$ is
(A) Zero
(B) $v B R \sqrt{2}$
(C) $v B R$
(D) $2 v B R$

Ankur S
Ankur S
Numerade Educator
01:25

Problem 60

A very long uniformly charged rod falls with a constant velocity $V$ through the centre of a circular loop. Then the magnitude of induced EMF in loop is (charge per unit length of $\operatorname{rod}=\lambda)$
(A) $\frac{\mu_{0}}{2 \pi} \lambda V^{2}$
(B) $\frac{\mu_{0}}{2} \lambda V^{2}$
(C) $\frac{\mu_{0}}{2 \lambda} V$
(D) Zero

Ankur S
Ankur S
Numerade Educator
01:39

Problem 61

A small square loop of wire of side $\ell$ is placed inside a large square loop of wire of side $L(L \gg \ell)$. The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to
(A) $\frac{l}{L}$
(B) $\frac{l^{2}}{L}$
(C) $\frac{L}{l}$
(D) $\frac{L^{2}}{l}$

Ankur S
Ankur S
Numerade Educator
02:27

Problem 62

In a uniform magnetic field of induction $B$, a wire in the form of semicircle of radius $r$ rotates about the diameter of the circle with angular frequency $\omega$. If the total resistance of the circuit is $R$, the mean power generated per period of rotation is
(A) $\frac{B \pi r^{2} \omega}{2 R}$
(B) $\frac{\left(B \pi r^{2} \omega\right)^{2}}{2 R}$
(C) $\frac{(B \pi r \omega)^{2}}{2 R}$
(D) $\frac{\left(B \pi r^{2} \omega\right)^{2}}{8 R}$

Ankur S
Ankur S
Numerade Educator
02:04

Problem 63

A rod of length $\ell$, negligible resistance, and mass $m$ slides on two horizontal frictionless rails of negligible resistance by hanging a block of mass $m_{1}$ with the help of insulating a massless string passing through fixed massless pulley (as shown in Fig. 16.51). If a constant magnetic field $B$ acts upwards perpendicular to the plane of the figure, the terminal velocity of hanging mass is
(A) $\frac{m_{1} g R}{B^{2} l^{2}}$ upward
(B) $\frac{m_{1} g R}{B^{2} l^{2}}$ downward
(C) $\frac{m_{1} g R}{2 B^{2} l^{2}}$ downward
(D) $\frac{m_{1} g R}{B^{2} l}$ downward

Ankur S
Ankur S
Numerade Educator
01:08

Problem 64

Magnetic field $B_{0}$ exists perpendicular inwards. The resistance of the loop is $R$. When the switch is closed, the current induced in the circuit is
(A) $\frac{B l v}{R}$
(B) $\frac{3 B l v}{R}$
(C) $\frac{2 B l v}{R}$
(D) Zero

Ankur S
Ankur S
Numerade Educator
01:27

Problem 65

In the circuit shown, each battery has $\mathrm{EMF}=5 \mathrm{~V}$. Then the magnetic field at $P$ is
(A) Zero
(B) $\frac{10 \mu_{0}}{R_{1}(4 \pi)(0.2)}$
(C) $\frac{20 \mu_{0}}{\left(R_{1}+R_{2}\right)(0.8 \pi)}$
(D) None of these

Ankur S
Ankur S
Numerade Educator
01:18

Problem 66

The material which shows the effect shown in Fig. 16.52, when placed in a uniform magnetic field is called
(A) Paramagnetic
(B) Diamagnetic
(C) Ferromagnetic
(D) Anti-ferromagnetic

Ankur S
Ankur S
Numerade Educator
02:17

Problem 67

A conducting ring of mass $2 \mathrm{~kg}$ and radius $0.5 \mathrm{~m}$ is placed on a smooth horizontal plane. The ring carries a current $i=4 \mathrm{~A}$. A horizontal magnetic field $B=10 \mathrm{~T}$ is switched on at time $t=0$ as shown in Fig. 16.53. The initial angular acceleration of the ring will be
(A) $40 \pi \mathrm{rad} / \mathrm{s}^{2}$
(B) $20 \pi \mathrm{rad} / \mathrm{s}^{2}$
(C) $5 \pi \mathrm{rad} / \mathrm{s}^{2}$
(D) $15 \pi \mathrm{rad} / \mathrm{s}^{2}$

Ankur S
Ankur S
Numerade Educator
01:09

Problem 68

The EMF induced in a 1 millihenry inductor in which the current changes from $5 \mathrm{~A}$ to $3 \mathrm{~A}$ in $10^{-3}$ second is
(A) $2 \times 10^{-6} \mathrm{~V}$
(B) $8 \times 10^{-6} \mathrm{~V}$
(C) $2 \mathrm{~V}$
(D) $8 \mathrm{~V}$

Ankur S
Ankur S
Numerade Educator
01:40

Problem 69

Conducting circular loop of radius $r$ is placed in $x-y$ plane in gravity free space as shown in Fig. 16.54, mass of the loop is $m$ and centre of the loop is at the origin. At $t=0$, a current $I$ starts flowing through the loop and a magnetic field $\vec{B}=B_{0}(\hat{i}+\hat{j})$ is switched on in the region (where $B_{0}$ is a constant). The angular acceleration of the loop due to the torque of magnetic field is
(A) $\frac{\sqrt{2} \pi B_{0} i}{m}$
(B) $\frac{2 \sqrt{2} \pi B_{0} i}{m}$
(C) $\frac{\pi B_{0} i}{m}$
(D) $\frac{\pi B_{0} i}{2 m}$

Hunza Gilgit
Hunza Gilgit
Numerade Educator
03:06

Problem 70

A direct current flowing through the winding of a long cylindrical solenoid of radius $R$ produces in it a uniform magnetic field of induction $B$. An electron flies into the solenoid along the radius between its turns (at right angles to the solenoid axis) at a velocity $v$ as shown in Fig. 16.55. After a certain time, the electron deflected by the magnetic field leaves the solenoid. Then the time $t$ during which the electron moves in the solenoid is
(A) $\frac{m}{e B} \tan ^{-1}\left(\frac{e B R}{m v}\right)$
(B) $\frac{2 m}{e B} \tan ^{-1}\left(\frac{e B R}{m v}\right)$
(C) $\frac{m}{e B} \tan ^{-1}\left(\frac{m v}{e B R}\right)$
(D) $\frac{2 m}{e B} \tan ^{-1}\left(\frac{m v}{e B R}\right)$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
00:59

Problem 71

A magnetized wire of moment $M$ is bent into an arc of a circle subtending an angle of $60^{\circ}$ at the centre, the new magnetic moment is
(A) $\frac{2 M}{\pi}$
(B) $\frac{M}{\pi}$
(C) $\frac{3 \sqrt{3} M}{\pi}$
(D) $\frac{3 M}{\pi}$

Nidhi Singhi
Nidhi Singhi
Numerade Educator
01:10

Problem 72

Total energy of electromagnetic waves in vacuum is given by the relation
(A) $\frac{1}{2} \cdot \frac{E^{2}}{\varepsilon_{0}}+\frac{B^{2}}{2 \mu_{0}}$
(B) $\frac{1}{2} \varepsilon_{0} E^{2}+\frac{1}{2} \mu_{0} B^{2}$
(C) $\frac{E^{2}+B^{2}}{c}$
(D) $\frac{1}{2} \varepsilon_{0} E^{2}+\frac{B^{2}}{2 \mu_{0}}$

Ankur S
Ankur S
Numerade Educator
01:36

Problem 73

An iron rod of cross-sectional area 4 sq $\mathrm{cm}$ is placed with its length parallel to a magnetic field of intensity $1600 \mathrm{amp} / \mathrm{m}$. The flux through the rod is $4 \times 10^{-4}$ weber. The permeability of the material of the rod is (In weber/amp-m).
(A) $0.625$
(B) $6.25$
(C) $0.625 \times 10^{-3}$
(D) None of these

Ankur S
Ankur S
Numerade Educator
01:16

Problem 74

An electron moves along the line $A B$ which lies in the same plane as a circular loop of conducting wire as shown in Fig. 16.56. The direction of the induced current in loop will be
(A) no current induced.
(B) clockwise.
(C) anti-clockwise.
(D) the current will change direction as the electron passes by.

Ankur S
Ankur S
Numerade Educator
01:52

Problem 75

A charged particle of mass $m$ and charge $q$ is projected into a uniform magnetic field of induction $B$ with speed $v$ which is perpendicular to $B$. The width of the magnetic field is $d$. the impulse imparted to the particle by the field is $(d<<m v / q B)$
$$
\begin{array}{ccccc}
q & \times & \times & \times & \times \\
\bullet^{\bullet} & \times & \times & \times \vec{B} \times \\
& \times & \times & \times & \times
\end{array}
$$
(A) $q B v$
(B) $m v / q B$
(C) $q B d$
(D) $2 m v^{2} / q B$

Ankur S
Ankur S
Numerade Educator
01:37

Problem 76

A circular ring is fixed in a gravitational field. A bar magnet is projected towards its centre as shown in Fig. $16.57$
(A) Initially, magnet experiences an acceleration and then it retards.
(B) Magnet starts to oscillate about centre of the ring.
(C) Magnet continues to move along the axis with constant velocity.
(D) The magnet retards and comes to rest finally.

Ankur S
Ankur S
Numerade Educator
02:55

Problem 77

Two charge particles are moving parallel to each other with velocities $2 \times 10^{8} \mathrm{~m} / \mathrm{s}$ and $1 \times 10^{8} \mathrm{~m} / \mathrm{s}$, respectively. The ratio of magnetic force between them and electrostatic force between them is
(A) $\frac{2}{9}$
(B) $\frac{1}{9}$
(C) $\frac{9}{2}$
(D) 9

Ankur S
Ankur S
Numerade Educator
00:57

Problem 78

There is a small metallic ring of radius $\ell_{0}$ having negligible resistance placed perpendicular to a constant magnetic field $B_{0}$. One end of a rod is hinged at the centre of ring $O$ and other end is placed on the ring. Now rod is rotated with constant angular velocity $\omega_{0}$ by some external agent and circuit is connected as shown in Fig. $16.58$; initially, switch is open and capacitor is uncharged. If switch $S$ is closed at $t=0$, then calculate heat loss from the resistor $R_{2}$ from $t=0$ to the instant when voltage across the capacitor becomes $V_{0}$. (Assume plane of ring to be horizontal and friction to be absent at all the contacts.) (Assume, $R_{2}=2 R_{1}, B_{0} l_{0}^{2} \omega_{0}=4 V_{0}$ )
(A) $\frac{1}{2} C V_{0}^{2}$
(B) $\frac{1}{6} C V_{0}^{2}$
(C) $\frac{2}{3} C V_{0}^{2}$
(D) $\frac{1}{3} C V_{0}^{2}$

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:48

Problem 79

A positive charge is passing through an electromagnetic field in which $\vec{E}$ and $\vec{B}$ are directed towards $y$-axis and $z$-axis, respectively. If a charged particle passes through the region undeviated, then its velocity is/are represented by (here $a, b$, and $c$ are constant)
(A) $\vec{v}=\frac{E}{B} \hat{i}+a \hat{j}$
(B) $\vec{v}=\frac{E}{B} \hat{i}+b \hat{k}$
(C) $\vec{v}=\frac{E}{B} \hat{i}+c \hat{i}$
(D) $\vec{v}=\frac{E}{B} \hat{i}$

Ankur S
Ankur S
Numerade Educator
02:02

Problem 80

A conducting $\operatorname{rod} A C$ of length $4 \ell$ is rotated about a point $O$ in a uniform magnetic field directed into the paper. $A O=\ell$ and $O C=3 \ell$. Then
(A) $V_{O}-V_{A}=\frac{B \omega l^{2}}{2}$
(B) $V_{O}-V_{A}=\frac{9}{2} B \omega l^{2}$
(C) $V_{A}-V_{C}=4 B \omega l^{2}$
(D) $V_{O}-V_{C}=\frac{9}{2} B \omega l^{2}$

Ankur S
Ankur S
Numerade Educator
03:41

Problem 81

Two straight conducting rails form a right angle where their ends are joined. A conducting bar in contact with the rails starts at the vertex at $t=0$ and moves with a constant velocity $v$ along them as shown in Fig. $16.59 .$ A magnetic field $B$ is directed into the page. The induced EMF in the circuit at any time $t$ is proportional to
(A) $t^{0}$
(B) $t$
(C) $v$
(D) $v^{2}$

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
01:32

Problem 82

In a cylindrical region of radius $R$, there exists a time varying magnetic field $B$ such that $\frac{d B}{d t}=k(>0)$. A charged particle having charge $q$ is placed at the point $P$ at a distance $d(>R)$ from its centre $O .$ Now, the particle is moved in the direction perpendicular to $O P$ (see Fig. 16.60) by an external agent up to infinity so that there is no gain in kinetic energy of the charged particle. Choose the correct statement/s.
(A) Work done by external agent is $\frac{q \pi R^{2}}{4} k$ if $d=2 R$
(B) Work done by external agent is $\frac{q \pi R^{2}}{8} k$ if $d=4 R$
(C) Work done by external agent is $\frac{q \pi R^{2}}{4} k$ if $d=4 R$
(D) Work done by external agent is $\frac{q \pi R^{2}}{4} k$ if $d=6 R$

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:26

Problem 83

The magnetic field perpendicular to the plane of conducting ring of radius $r$ changes at the rate $\frac{d B}{d t}=\alpha$. Then
(A) EMF induced in the ring is $\pi r^{2} \alpha$.
(B) EMF induced in the ring is $2 \pi r \alpha$.
(C) The potential difference between diametrically opposite points on the ring is half of induced EMF.
(D) All points on the ring are at same potential.

Ankur S
Ankur S
Numerade Educator
01:38

Problem 84

A uniform conducting ring of mass $\pi \mathrm{kg}$ and radius $1 \mathrm{~m}$ is kept on smooth horizontal table. A uniform but time varying magnetic field $B=\left(\hat{i}+t^{2} \hat{j}\right)$ Tesla is present in the region. (Where $t$ is time in seconds). Resistance of ring is $2 \Omega .$ Then, $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
Net magnetic force (in Newton) on conducting ring as function of time is
(A) $2 \pi^{2} t$
(B) $2 \pi^{2} t^{2}$
(C) $2 \pi^{2} t^{3}$
(D) Zero

Ankur S
Ankur S
Numerade Educator
01:55

Problem 85

A uniform conducting ring of mass $\pi \mathrm{kg}$ and radius $1 \mathrm{~m}$ is kept on smooth horizontal table. A uniform but time varying magnetic field $B=\left(\hat{i}+t^{2} \hat{j}\right)$ Tesla is present in the region. (Where $t$ is time in seconds). Resistance of ring is $2 \Omega .$ Then, $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
Time (in second) at which ring start toppling is
(A) $\frac{10}{\pi}$
(B) $\frac{20}{\pi}$
(C) $\frac{5}{\pi}$
(D) $\frac{25}{\pi}$

Ankur S
Ankur S
Numerade Educator
01:46

Problem 86

A uniform conducting ring of mass $\pi \mathrm{kg}$ and radius $1 \mathrm{~m}$ is kept on smooth horizontal table. A uniform but time varying magnetic field $B=\left(\hat{i}+t^{2} \hat{j}\right)$ Tesla is present in the region. (Where $t$ is time in seconds). Resistance of ring is $2 \Omega .$ Then, $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
Heat generated (in $\mathrm{kJ}$ ) through the ring till the instant when ring starts toppling is
(A) $\frac{1}{3 \pi}$
(B) $\frac{2}{\pi}$
(C) $\frac{2}{3 \pi}$
(D) $\frac{1}{\pi}$

Ankur S
Ankur S
Numerade Educator
01:09

Problem 87

A uniform conducting ring of mass $\pi \mathrm{kg}$ and radius $1 \mathrm{~m}$ is kept on smooth horizontal table. A uniform but time varying magnetic field $B=\left(\hat{i}+t^{2} \hat{j}\right)$ Tesla is present in the region. (Where $t$ is time in seconds). Resistance of ring is $2 \Omega .$ Then, $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
Induced electric field (in volt/meter) at the circumference of ring at the instant ring starts toppling is
(A) $\frac{10}{\pi}$
(B) $\frac{20}{\pi}$
(C) $\frac{5}{\pi}$
(D) $\frac{25}{\pi}$

Ankur S
Ankur S
Numerade Educator
01:47

Problem 88

A plane loop is shaped as shown in Fig. $16.61$ with radii $a=20 \mathrm{~cm}$ and $b=10 \mathrm{~cm}$ and is placed in a uniform time varying magnetic field $B=(20+10 t) \mathrm{T}$, where $t$ is the time in second. Answer the following questions based on the above statement
The induced EMF in the loop is
(A) $0.942 \mathrm{~V}$
(B) $1.57 \mathrm{~V}$
(C) $0.157 \mathrm{~V}$
(D) $0.0942 \mathrm{~V}$

Ankur S
Ankur S
Numerade Educator
01:06

Problem 89

A plane loop is shaped as shown in Fig. $16.61$ with radii $a=20 \mathrm{~cm}$ and $b=10 \mathrm{~cm}$ and is placed in a uniform time varying magnetic field $B=(20+10 t) \mathrm{T}$, where $t$ is the time in second. Answer the following questions based on the above statement
The maximum charge on each capacitor is
(A) $4.71 \times 10^{-6} \mathrm{C}$
(B) $0.471 \times 10^{-6} \mathrm{C}$
(C) $52 \times 10^{-6} \mathrm{C}$
(D) $5.2 \times 10^{-6} \mathrm{C}$

Ankur S
Ankur S
Numerade Educator
01:04

Problem 90

A plane loop is shaped as shown in Fig. $16.61$ with radii $a=20 \mathrm{~cm}$ and $b=10 \mathrm{~cm}$ and is placed in a uniform time varying magnetic field $B=(20+10 t) \mathrm{T}$, where $t$ is the time in second. Answer the following questions based on the above statement
The energy stored in each capacitor is
(A) $1.11 \times 10^{-7} \mathrm{~J}$
(B) $11.1 \times 10^{-7} \mathrm{~J}$
(C) $111 \times 10^{-7} \mathrm{~J}$
(D) $0.111 \times 10^{-7} \mathrm{~J}$

Ankur S
Ankur S
Numerade Educator
01:28

Problem 91

Net force on a current carrying loop kept in uniform magnetic field is zero and the torque on the loop $\vec{\tau}=\vec{M} \times \vec{B}$, where $M$ and $B$ are magnetic dipole moment and magnetic field intensity, respectively. If it is free to rotate, then it will rotates about an axis passing through its centre of mass and parallel to $\vec{\tau}$. Potential energy of the loop is given by $U=-\vec{M} \cdot \vec{B}$. Assume a current carrying ring with its centre at the origin and having moment of inertia $2 \times 10^{-2} \mathrm{~kg}-\mathrm{m}^{2}$ about an axis passing through one of its diameter and magnetic moment $\vec{M}=(3 \hat{i}-4 \hat{j}) \mathrm{Am}^{2}$. At time $t=0$, a magnetic field $\vec{B}=(4 \hat{i}-3 \hat{j}) T$ is switched on. Then
Torque acting on the loop is
(A) Zero
(B) $25 \hat{k} \mathrm{Nm}$
(C) $16 \hat{k} \mathrm{Nm}$
(D) $10 \hat{k} \mathrm{Nm}$

Ankur S
Ankur S
Numerade Educator
01:06

Problem 92

Net force on a current carrying loop kept in uniform magnetic field is zero and the torque on the loop $\vec{\tau}=\vec{M} \times \vec{B}$, where $M$ and $B$ are magnetic dipole moment and magnetic field intensity, respectively. If it is free to rotate, then it will rotates about an axis passing through its centre of mass and parallel to $\vec{\tau}$. Potential energy of the loop is given by $U=-\vec{M} \cdot \vec{B}$. Assume a current carrying ring with its centre at the origin and having moment of inertia $2 \times 10^{-2} \mathrm{~kg}-\mathrm{m}^{2}$ about an axis passing through one of its diameter and magnetic moment $\vec{M}=(3 \hat{i}-4 \hat{j}) \mathrm{Am}^{2}$. At time $t=0$, a magnetic field $\vec{B}=(4 \hat{i}-3 \hat{j}) T$ is switched on. Then
Angular acceleration of the ring at time $t=0$ (in $\mathrm{rad} / \mathrm{s}^{2}$ ) is
(A) 5000
(B) 1250
(C) 2500
(D) Zero

Ankur S
Ankur S
Numerade Educator
02:13

Problem 93

Net force on a current carrying loop kept in uniform magnetic field is zero and the torque on the loop $\vec{\tau}=\vec{M} \times \vec{B}$, where $M$ and $B$ are magnetic dipole moment and magnetic field intensity, respectively. If it is free to rotate, then it will rotates about an axis passing through its centre of mass and parallel to $\vec{\tau}$. Potential energy of the loop is given by $U=-\vec{M} \cdot \vec{B}$. Assume a current carrying ring with its centre at the origin and having moment of inertia $2 \times 10^{-2} \mathrm{~kg}-\mathrm{m}^{2}$ about an axis passing through one of its diameter and magnetic moment $\vec{M}=(3 \hat{i}-4 \hat{j}) \mathrm{Am}^{2}$. At time $t=0$, a magnetic field $\vec{B}=(4 \hat{i}-3 \hat{j}) T$ is switched on. Then
Maximum angular velocity of the ring (in $\mathrm{rad} / \mathrm{s})$ will be
(A) $50 \sqrt{2}$
(B) $25 \sqrt{2}$
(C) $100 \sqrt{2}$
(D) $150 \sqrt{2}$

Ankur S
Ankur S
Numerade Educator
01:37

Problem 94

Two parallel vertical rails $A B$ and $C D$, separated by $1 \mathrm{~m}$, are connected at two ends by resistances $R_{1}$ and $R_{2}$ as shown in Fig. 16.62. A horizontal metallic bar of mass $0.2 \mathrm{~kg}$ slides without friction vertically down the rails under the action of gravity. There is a uniform horizontal magnetic field of $0.6 \mathrm{~T}$ perpendicular to the plane of the rails. It is observed that when the terminal velocity is achieved, the powers dissipated in $R_{1}$ and $R_{2}$ are $0.76$ watt and $1.2$ watt, respectively.
Terminal velocity of bar is
(A) $4 \mathrm{~m} / \mathrm{s}$
(B) $3 \mathrm{~m} / \mathrm{s}$
(C) $2 \mathrm{~m} / \mathrm{s}$
(D) $1 \mathrm{~m} / \mathrm{s}$

Ankur S
Ankur S
Numerade Educator
01:57

Problem 95

Two parallel vertical rails $A B$ and $C D$, separated by $1 \mathrm{~m}$, are connected at two ends by resistances $R_{1}$ and $R_{2}$ as shown in Fig. 16.62. A horizontal metallic bar of mass $0.2 \mathrm{~kg}$ slides without friction vertically down the rails under the action of gravity. There is a uniform horizontal magnetic field of $0.6 \mathrm{~T}$ perpendicular to the plane of the rails. It is observed that when the terminal velocity is achieved, the powers dissipated in $R_{1}$ and $R_{2}$ are $0.76$ watt and $1.2$ watt, respectively.
Value of resistance $R_{1}$ is
(A) $0.12 \Omega$
(B) $0.24 \Omega$
(C) $0.47 \Omega$
(D) $0.96 \Omega$

Ankur S
Ankur S
Numerade Educator
01:57

Problem 96

Two parallel vertical rails $A B$ and $C D$, separated by $1 \mathrm{~m}$, are connected at two ends by resistances $R_{1}$ and $R_{2}$ as shown in Fig. 16.62. A horizontal metallic bar of mass $0.2 \mathrm{~kg}$ slides without friction vertically down the rails under the action of gravity. There is a uniform horizontal magnetic field of $0.6 \mathrm{~T}$ perpendicular to the plane of the rails. It is observed that when the terminal velocity is achieved, the powers dissipated in $R_{1}$ and $R_{2}$ are $0.76$ watt and $1.2$ watt, respectively.
Value of resistance $R_{2}$ is
(A) $0.1 \Omega$
(B) $0.2 \Omega$
(C) $0.3 \Omega$
(D) $0.4 \Omega$

Ankur S
Ankur S
Numerade Educator
01:49

Problem 97

A magnetic field $\vec{B}=\left(\frac{B_{0} y}{a}\right) \hat{k}$ is into the paper in the $+z$ direction. $B_{0}$ and $a$ are positive constants. A square loop $E F G H$ of side $a$, mass $m$, and resistance $R$, in $x-y$ plane, starts falling under the influence of gravity. Assume $x$-axis is horizontal and $y$ is vertically downward.
The magnitude and direction of the induced current in the loop when its speed is $v$ is
(A) $\frac{B_{0} a v}{R}$, anti-clockwise
(B) $\frac{B_{0} a v}{R}$, clockwise
(C) $\frac{B_{0} v}{a R}$, anti-clockwise
(D) None of these

Ankur S
Ankur S
Numerade Educator
02:56

Problem 98

A magnetic field $\vec{B}=\left(\frac{B_{0} y}{a}\right) \hat{k}$ is into the paper in the $+z$ direction. $B_{0}$ and $a$ are positive constants. A square loop $E F G H$ of side $a$, mass $m$, and resistance $R$, in $x-y$ plane, starts falling under the influence of gravity. Assume $x$-axis is horizontal and $y$ is vertically downward.
The magnitude and direction of the net Lorentz force, acting on the loop when its speed is $v$, is
(A) $\frac{B_{0} a^{2} v}{R}$, upward
(B) $\frac{B_{0} a^{2} v}{R}$, downward
(C) $\frac{B_{0}^{2} a^{2} v}{R}$, downward
(D) $\frac{B_{0}^{2} a^{2} v}{R}$, upward

Ankur S
Ankur S
Numerade Educator
03:14

Problem 99

A magnetic field $\vec{B}=\left(\frac{B_{0} y}{a}\right) \hat{k}$ is into the paper in the $+z$ direction. $B_{0}$ and $a$ are positive constants. A square loop $E F G H$ of side $a$, mass $m$, and resistance $R$, in $x-y$ plane, starts falling under the influence of gravity. Assume $x$-axis is horizontal and $y$ is vertically downward.
The expression for the speed of the loop $v(t)$ is
(A) $\frac{m g}{B_{0}^{2} a^{2}}\left(1-e^{-\frac{B^{2} a^{2} t}{m R}}\right)$
(B) $\frac{R m g}{B_{0}^{2} a^{2}}\left(1-e^{-\frac{B^{2} a^{2} t}{m R}}\right)$
(C) $\frac{R m g}{B_{0}^{2} a^{2}}\left(e^{-\frac{B_{0}^{2} a^{2} t}{m R}}\right)$
(D) None of these

Ankur S
Ankur S
Numerade Educator
02:05

Problem 100

A magnetic field $\vec{B}=\left(\frac{B_{0} y}{a}\right) \hat{k}$ is into the paper in the $+z$ direction. $B_{0}$ and $a$ are positive constants. A square loop $E F G H$ of side $a$, mass $m$, and resistance $R$, in $x-y$ plane, starts falling under the influence of gravity. Assume $x$-axis is horizontal and $y$ is vertically downward.
Acceleration of the loop when its speed is half of its terminal speed is
(A) $\frac{g}{2}$
(B) $g e^{-2}$
(C) $g e^{-1 / 2}$
(D) $g e^{-4}$

Ankur S
Ankur S
Numerade Educator
03:40

Problem 101

A uniform but time varying magnetic field $B(t)$ exists in a cylindrical region of radius $a$ and is directed into the plane of the paper, as shown in Fig. $16.63$. Magnetic field decreases at constant rate inside the region. If $r$ is the distance from axis of cylindrical region, then
Column-I Column-II
(A) Induced electric field at 1 . Directed along 3 point $\bar{A}$
(B) Induced electric field at
2. Directed along 1 point $B$
(C) Force on an electron
3. Increases as $r$ placed at point $A$
(D) Force on an electron
4. Decreases as $1 / r$ placed at point $B$

Ankur S
Ankur S
Numerade Educator
02:55

Problem 102

A circular current carrying loop of 100 turns and radius $10 \mathrm{~cm}$ is placed in $x-y$ plane as shown. A uniform magnetic field $\vec{B}=(-\hat{i}+\hat{k})$ tesla is present in the region. If current in the loop is $5 \mathrm{~A}$,
Column-I Column-II
(A) Magnitude and direction of 1. Zero magnetic moment (in $\mathrm{A}-\mathrm{m}$ ) of the loop
(B) Magnitude and direction of
2. $5 \pi$ torque (in $\mathrm{N}-\mathrm{m}$ ) on the loop
(C) Magnitude and direction
3. along positive of net force (in $\mathrm{N}$ ) on the $z$-axis current loop
(D) Direction of magnetic field
4. along of loop at the centre negative $y$-axis

Ankur S
Ankur S
Numerade Educator
02:43

Problem 103

A square loop is placed near a long straight current carrying wire as shown.
Column-I Column-II
(A) If current is
1. Induced current in increased loop is clockwise
(B) If current is
2. Induced current in decreased $\quad$ loop is anti-clockwise
(C) If loop is moved
3. Wire will attract the away from the wire loop
(D) If loop is moved
4. Wire will repel the towards the wire

Ankur S
Ankur S
Numerade Educator
01:35

Problem 104

Magnetic flux in a circular coil of resistance $10 \Omega$ and radius $7 / 44 \mathrm{~m}$ changes with time as shown in Fig. 16.64. \otimes direction indicates a direction perpendicular to a paper inwards.
Column-I Column-II
(A) At ls induced current is
1. Clockwise (in A)
(B) At 7 s induced current is
2. Anti-clockwise (in A)
(C) At 1 s induced electric filed
3. 5 at circumference is (in $\mathrm{N} / \mathrm{C}$ )
(D) Maximum induced EMF in
4. $0.5$ coil within $t=16 \mathrm{~s}$ (in volt)

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:10

Problem 105

Which of the effect (s) given in column-II will be produced by a loop mentioned in column-I
Column-I Column-II
(A) Stationary dielectric
1. Electric field ring having uniform charge
(B) Dielectric ring having
2. Magnetostatic field uniform charge is rotating with constant angular velocity
(C) A constant current $I_{0}$
3. Time-dependent in the loop induced electric field outside the loop
(D) Time varying
4. Magnetic moment sinusoidal current in in the loop the loop $I=I_{0} \cos \omega t$

Hunza Gilgit
Hunza Gilgit
Numerade Educator
01:31

Problem 106

Assertion: In Fig. $16.65$, just after closing the switch the potential drop across inductor is maximum. Reason: The rate of change of current just after closing the switch is maximum.
(A) $\mathrm{A}$
(B) B
(C) $\mathrm{C}$
(D) D

Ankur S
Ankur S
Numerade Educator
01:18

Problem 107

Assertion: A charged particle is moving in a circle with constant speed in uniform magnetic field. If we increase the speed of particle to twice, its acceleration will become four times.
Reason: In circular path with constant speed, acceleration is given by $\frac{v^{2}}{R}$.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\overline{\mathrm{C}}$
(D) D

Ankur S
Ankur S
Numerade Educator
01:25

Problem 108

Assertion: A charged particle is accelerated by a potential difference of $V$ volts. It then enters perpendicularly to a uniform magnetic field. It rotates in a circle. Its angular momentum about centre is say $L$. Now if $V$ is doubled, $L$ also becomes double.
Reason: If $V$ is doubled, kinetic energy will become two times and therefore, but $L$ remains same.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\overline{\mathrm{C}}$
(D) D

Ankur S
Ankur S
Numerade Educator
01:17

Problem 109

Assertion: When a test charge moves through a magnetic field, its momentum changes but kinetic energy remains constant.
Reason: The magnetic force acts as a centripetal force, which is perpendicular to the instantaneous velocity and so does no work.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\overline{\mathrm{C}}$
(D) D

Ankur S
Ankur S
Numerade Educator
01:51

Problem 110

Assertion: When a magnet is made to fall freely through a closed conducting coil, its acceleration is always less than acceleration due to gravity. Reason: Current induced in the coil opposes the motion of the magnet, as per Lenz's law.
(A) $\mathrm{A}$
(B) B
(C) $\overline{\mathrm{C}}$
(D) D

Ankur S
Ankur S
Numerade Educator
01:26

Problem 111

Assertion: An inductor acts as perfect conductor for DC at steady state.
Reason: DC remains constant in magnitude.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Ankur S
Ankur S
Numerade Educator
01:14

Problem 112

Assertion: In the phenomenon of mutual induction, self-induction of each of the coil persists.
Reason: Self-induction arises when strength of current in one coil changes. In mutual induction, current is changing in both the individual coils.
(A) $\mathrm{A}$
(B) $\mathrm{B}$
(C) $\overline{\mathrm{C}}$
(D) D

Ankur S
Ankur S
Numerade Educator
01:13

Problem 113

Assertion: A charged particle moves perpendicular to a uniform magnetic field then its momentum remains constant.
Reason: Magnetic force acts perpendicular to the velocity of the particle.
(A) A
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Ankur S
Ankur S
Numerade Educator
01:23

Problem 114

Assertion: A solenoid is connected to an ideal cell. If there is no resistance in the circuit, then rate of change of current $\left(\frac{d I}{d t}\right)$ will decrease.
Reason: If a solenoid is connected to a cell through a resistance, potential difference across the solenoid decreases.
(A) A
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Ankur S
Ankur S
Numerade Educator
01:34

Problem 115

Assertion: A charged particle at rest experiences no electromagnetic force.
Reason: The electric and magnetic field must be zero.
(A) A
(B) $\mathrm{B}$
(C) $\mathrm{C}$
(D) D

Ankur S
Ankur S
Numerade Educator
02:49

Problem 116

A capacitor of capacitance $C=\frac{18}{\pi} \mathrm{mH}$ having initial charge $Q_{0}$ connected to an inductor of inductance $L=\frac{18}{\pi} \mathrm{mH}$ at $t=0$. Find the time (in milli second) after energy stored in electric field is three times energy stored in magnetic field.

Ankur S
Ankur S
Numerade Educator
03:03

Problem 117

A coil of inductance $1 H$ and resistance $10 \Omega$ is connected to a resistance-less battery of EMF $50 \mathrm{~V}$ at time $t=0 .$ The ratio of rate at which magnetic energy is stored in the coil to the rate at which energy is supplied by the battery at $t=0.1 \mathrm{~s} .$ is $x \times 10^{-2}$. Find the value of $x$. (Given $\left.\frac{1}{e}=0.37\right)$

Ankur S
Ankur S
Numerade Educator
01:37

Problem 118

Two parallel vertical metallic rails $A B$ and $C D$ are separated by $1 \mathrm{~m}$. They are connected at the two ends by resistances $R_{1}$ and $R_{2}$ as shown. A horizontal metallic bar $P Q$ of mass $0.2 \mathrm{~kg}$ slides without friction, vertically down the rails under the action of gravity. There is uniform horizontal magnetic field of $0.6 \mathrm{~T}$ perpendicular to plane of the rails. It is observed that 12 when the terminal velocity attained, the power dissipated in $R_{1}$ and $R_{2}$ are $0.76 \mathrm{~W}$ and $1.2 \mathrm{~W}$, respectively. Find the terminal velocity of bar in $\mathrm{m} / \mathrm{s}\left(\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)$.

Ankur S
Ankur S
Numerade Educator
03:26

Problem 119

Figure $16.66$ shows four rods having $\lambda=0.5 \Omega / \mathrm{m}$ resistance per unit length. The arrangement is kept in a magnetic field of constant magnitude $B=2 \mathrm{~T}$ and directed perpendicular to the plane of the figure and directed inwards. Initially, the rods form a square of side length $\ell=15 \mathrm{~m}$ as shown. Now each wire starts moving with constant velocity $v=5 \mathrm{~m} / \mathrm{s}$ towards opposite wire. Find the force required in newton on each wire to keep its velocity constant at $t=1 \mathrm{~s}$.

Ankur S
Ankur S
Numerade Educator
02:23

Problem 120

A block is attached to the ceiling by a spring that has a force constant $k=200 \mathrm{~N} / \mathrm{m}$. A conducting rod is rigidly attached to the block. The combined mass of the block and the rod is $m=0.3 \mathrm{~kg}$. The rod can slide without friction along two vertical parallel rails, which are a distance $\ell=1 \mathrm{~m}$ apart. A capacitor of known capacitance $C=500 \mu \mathrm{F}$ is attached to the rails by the wires. The entire system is placed in a uniform magnetic field $B=20 \mathrm{~T}$ directed as shown. Find the angular frequency (in $\mathrm{rad} / \mathrm{s}$ ) of the vertical oscillations of the block. Neglect the self-inductance and electrical resistance of the rod and all wires.

Prem Bijarniya
Prem Bijarniya
Numerade Educator
02:37

Problem 121

A loop is formed by two parallel conductors connected by a solenoid with inductance $L=2 H$ and a conducting rod of mass $m=8 \mathrm{~kg}$ which can freely (without friction) slide over the conductors. The conductors are located in a horizontal plane and in a uniform vertical magnetic field $B=\pi T$. The distance between the conductors is $\ell=2 \mathrm{~m}$. At the moment, $t=0$, the rod is imparted on initial velocity $v_{0}=2 \mathrm{~m} / \mathrm{s}$ directed to the right. Find the time period of oscillation of rod in second if the resistance of loop is negligible.

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
03:12

Problem 122

A non-conducting non-magnetic rod having circular cross-section of radius $R$ is suspended from a rigid support as shown in Fig. 16.67. A light and small coil of 300 turns is wrapped tightly at the left end of the rod where uniform magnetic field $B$ exists in vertically downward direction. Air of density $\rho$ hits the half of the right part of the rod with velocity $v$ as shown in Fig. 16.67. What should be current in clockwise direction (as seen from $O$ ) in the coil so that rod remains horizontal? Give answer in $\mathrm{mA}$, given $\frac{2}{L v} \sqrt{\frac{\pi R B}{\rho}}=1 \mathrm{~A}^{-1 / 2}$

Ankur S
Ankur S
Numerade Educator
02:04

Problem 123

A uniform disc of radius $R$ having charge $Q$ distributed uniformly all over its surface is placed on a smooth horizontal surface. A magnetic field, $B=k x t^{2}$, where $k$ is a constant, $x$ is the distance (in metre) from the centre of the disc, and $t$ is the time (in second) is switched on perpendicular to the plane of the disc. Find the torque (in $\mathrm{N}-\mathrm{m}$ ) acting on the disc after $15 \mathrm{~s}$ (Take $4 k Q=1$ S.I. unit and $R=1 \mathrm{~m}$ ).

Prem Bijarniya
Prem Bijarniya
Numerade Educator
01:10

Problem 124

The power factor of an AC circuit having resistance $(R)$ and inductance $(L)$ connected in series and an angular velocity $\omega$ is
(A) $R / \omega L$
(B) $R /\left(R^{2}+\omega^{2} L^{2}\right)^{1 / 2}$
(C) $\omega L / R$
(D) $R /\left(R^{2}-\omega^{2} L^{2}\right)^{1 / 2}$

Ankur S
Ankur S
Numerade Educator
01:25

Problem 125

A conducting square loop of side $L$ and resistance $R$ moves in its plane with a uniform velocity verpendicular to one of its sides. A magnetic induction $\mathrm{B}$ constant in time and space, pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field, as shown in Fig. $16.68$. The induced EMF is
(A) Zero
(B) $\mathrm{RvB}$
(C) $\mathrm{VBL} / \mathrm{R}$
(D) VBL

Ankur S
Ankur S
Numerade Educator
01:11

Problem 126

The inductance between $\mathrm{A}$ and $\mathrm{D}$ is
(A) $3.66 \mathrm{H}$
(B) $9 \mathrm{H}$
(C) $0.66 \mathrm{H}$
(D) $1 \mathrm{H}$

Ankur S
Ankur S
Numerade Educator
01:19

Problem 127

In a transformer, number of turns in primary coil are 140 and that of the secondary coil are 280 . If current in primary coil is $4 \mathrm{~A}$, then that of the secondary coil is
(A) $4 \mathrm{~A}$
(B) $2 \mathrm{~A}$
(C) $6 \mathrm{~A}$
(D) $10 \mathrm{~A}$

Ankur S
Ankur S
Numerade Educator
01:16

Problem 128

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon
(A) the rates at which currents are changing in the two coils.
(B) relative position and orientation of the two coils.
(C) the materials of the wires of the coils.
(D) the currents in the two coils.

Ankur S
Ankur S
Numerade Educator
01:10

Problem 129

When the current changes from $+2 \mathrm{~A}$ to $-2 \mathrm{~A}$ in $0.05$ second, an EMF of $8 \mathrm{~V}$ is induced in a coil. The coefficient of self-induction of the coil is
(A) $0.2 \mathrm{H}$
(B) $0.4 \mathrm{H}$
(C) $0.8 \mathrm{H}$
(D) $0.1 \mathrm{H}$

Ankur S
Ankur S
Numerade Educator
01:13

Problem 130

In an oscillating LC circuit, the maximum charge on the capacitor is $Q$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is
(A) $\frac{Q}{2}$
(B) $\frac{Q}{\sqrt{3}}$
(C) $\frac{Q}{\sqrt{2}}$
(D) $Q$

Ankur S
Ankur S
Numerade Educator
01:26

Problem 131

The core of any transformer is laminated so as to
(A) reduce the energy loss due to eddy currents.
(B) make it light weight.
(C) make it robust and strong.
(D) increase the secondary voltage.

Ankur S
Ankur S
Numerade Educator
01:22

Problem 132

Alternating current cannot be measured by DC ammeter because
(A) Average value of current for complete cycle is zero.
(B) AC changes direction.
(C) AC cannot pass through DC ammeter.
(D) DC ammeter will get damaged.

Ankur S
Ankur S
Numerade Educator
01:07

Problem 133

In an LCR series AC circuit, the voltage across each of the components, $L, C$, and $R$ is $50 \mathrm{~V}$. The voltage across the LC combination will be
(A) $100 \mathrm{~V}$
(B) $50 \sqrt{2} \mathrm{~V}$
(C) $50 \mathrm{~V}$
(D) $0 \mathrm{~V}$ (zero)

Ankur S
Ankur S
Numerade Educator
01:44

Problem 134

A coil having $n$ turns and resistance $R \Omega$ is connected with a galvanometer of resistance $4 R \Omega$. This combination is moved in time $t$ seconds from a magnetic field $W_{1}$ weber to $W_{2}$ weber. The induced current in the circuit is
(A) $-\frac{\left(W_{2}-W_{1}\right)}{R n t}$
(B) $-\frac{n\left(W_{2}-W_{1}\right)}{5 R t}$
(C) $-\frac{\left(W_{2}-W_{1}\right)}{5 R n t}$
(D) $-\frac{n\left(W_{2}-W_{1}\right)}{R t}$

Ankur S
Ankur S
Numerade Educator
03:06

Problem 135

In a uniform magnetic field of induction $B$, a wire in the form of a semicircle of radius $r$ rotates about the diameter of the circle with an angular frequency $\omega$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $R$, the mean power generated per period of rotation is
(A) $\frac{(B \pi r \omega)^{2}}{2 R}$
(B) $\frac{\left(B \pi r^{2} \omega\right)^{2}}{8 R}$
(C) $\frac{B \pi r^{2} \omega}{2 R}$
(D) $\frac{\left(B \pi r \omega^{2}\right)^{2}}{8 R}$

Ankur S
Ankur S
Numerade Educator
01:19

Problem 136

In a LCR circuit, capacitance is changed from $\mathrm{C}$ to $2 \mathrm{C}$, For the resonant frequency to remain unchanged, the inductance should be changed from $L$ to
(A) $\mathrm{L} / 2$
(B) $2 \mathrm{~L}$
(C) $4 \mathrm{~L}$
(D) $\underline{L} / 4$

Ankur S
Ankur S
Numerade Educator
01:10

Problem 137

A metal conductor of length $1 \mathrm{~m}$ rotates vertically about one of its ends at angular velocity 5 radians per second. If the horizontal component of earth's magnetic field is $0.2 \times 10^{-4} \mathrm{~T}$, then the EMF developed between the two ends of the conductor is
(A) $5 \mathrm{mV}$
(B) $50 \mu \mathrm{V}$
(C) $5 \mu \mathrm{V}$
(D) $50 \mathrm{mV}$

Ankur S
Ankur S
Numerade Educator
01:15

Problem 138

One conducting $U$ tube can slide inside another as shown in Fig. 16.69, maintaining electrical contacts between the tubes. The magnetic field $B$ is perpendicular to the plane of Fig. 16.69. If each tube moves towards the other at a constant speed $\mathrm{v}$, then the EMF induced in the circuit in terms of $B, \ell$, and $v$, where $\ell$, the width of each tube, will be
(A) $-B l v$
(B) $B l v$
(C) $2 \mathrm{Blv}$
(D) Zero

Ankur S
Ankur S
Numerade Educator
01:17

Problem 139

The self-inductance of the motor of an electric fan is $10 \mathrm{H}$. In order to impart maximum power at $50 \mathrm{~Hz}$, it should be connected to a capacitance of
(A) $8 \mu \mathrm{F}$
(B) $4 \mu \mathrm{F}$
(C) $2 \mu \mathrm{F}$
(D) $1 \mu \mathrm{F}$

Ankur S
Ankur S
Numerade Educator
01:07

Problem 140

The phase difference between the alternating current and EMF is $\frac{\pi}{2}$. Which of the following cannot be the constituent of the circuit?
(A) $\mathrm{R}, \mathrm{L}$
(B) C alone
(C) L alone
(D) $\mathrm{L}, \mathrm{C}$

Ankur S
Ankur S
Numerade Educator
01:16

Problem 141

A circuit has a resistance of 12 ohm and an impedance of $15 \Omega$. The power factor of the circuit will be
(A) $0.4$
(B) $0.8$
(C) $0.125$
(D) $1.25$

Ankur S
Ankur S
Numerade Educator
01:48

Problem 142

A coil of inductance $300 \mathrm{mH}$ and resistance $2 \Omega$ is connected to a source of voltage $2 \mathrm{~V}$. The current reaches half of its steady state value in
(A) $0.1 \mathrm{~s}$
(B) $0.05 \mathrm{~s}$
(C) $0.3 \mathrm{~s}$
(D) $0.15 \mathrm{~s}$

Ankur S
Ankur S
Numerade Educator
01:33

Problem 143

Which of the following units denotes the dimension $\frac{M L^{2}}{Q^{2}}$, where $Q$ denotes the electric charge?
(A) $\mathrm{Wb} / \mathrm{m}^{2}$
(B) Henry (H)
(C) $\mathrm{H} / \mathrm{m}^{2}$
(D) Weber ( $\mathrm{Wb}$ )

Ankur S
Ankur S
Numerade Educator
01:57

Problem 144

In a series resonant LCR circuit, the voltage across $R$ is $100 \mathrm{~V}$ and $R=1 k \Omega$ with $C=2 \mu \mathrm{F}$. The resonant frequency $\omega$ is $200 \mathrm{rad} / \mathrm{s}$. At resonance, the voltage across $L$ is
(A) $2.5 \times 10^{-2} \mathrm{~V}$
(B) $40 \mathrm{~V}$
(C) $250 \mathrm{~V}$
(D) $4 \times 10^{-3} \mathrm{~V}$

Ankur S
Ankur S
Numerade Educator
01:18

Problem 145

In an AC generator, a coil with $\mathrm{N}$ turns, all of the same area A and total resistance $\mathrm{R}$, rotates with frequency $\omega$ is a magnetic field $\mathrm{B}$. The maximum value of EMF generated in the coil is
(A) N.A.B.R. $\omega$
(B) N.A.B
(C) N.A.B.R.
(D) N.A.B $\omega$

Ankur S
Ankur S
Numerade Educator
01:10

Problem 146

The flux linked with a coil at my any instant $t$ is given by $\phi=10 t^{2}-50 t+250$ The induced EMF at $t=3 \mathrm{~s}$ is
(A) $-190 \mathrm{~V}$
(B) $-10 \mathrm{~V}$
(C) $10 \mathrm{~V}$
(D) $190 \mathrm{~V}$

Ankur S
Ankur S
Numerade Educator
02:03

Problem 147

An inductor $(L=100 \mathrm{mH})$, a resistor $(R=100 \Omega$ ), and a battery $(E=100 \mathrm{~V})$ are initially connected in series as shown in Fig. 16.70. After a long time, the battery is disconnected after short circuiting the points $A$ and $B$. The current in the circuit $1 \mathrm{~ms}$ after the short circuit is
(A) $1 / e \mathrm{Aq}$
(B) $\mathrm{e} \mathrm{A}$
(C) $0.1 \mathrm{~A}$
(D) $1 \mathrm{~A}$

Ankur S
Ankur S
Numerade Educator
01:26

Problem 148

In an AC circuit, the voltage applied is $E=E_{0} \sin \omega t$. Theresultingcurrent inthecircuit is $I=I_{0} \sin \left(\omega t-\frac{\pi}{2}\right)$. The power consumption in the circuit is given by
(A) $P=\sqrt{2} E_{0} I_{0}$
(B) $P=\frac{E_{0} I_{0}}{\sqrt{2}}$
(C) $P=0$
(D) $P=\frac{E_{0} I_{0}}{2}$

Ankur S
Ankur S
Numerade Educator
01:32

Problem 149

An ideal coil of $10 \mathrm{H}$ is connected in series with a resistance of $5 \Omega$ and a battery of $5 \mathrm{~V} .2$ second after the connection is made. The current flowing in ampere in the circuit is
(A) $\left(1-e^{-1}\right)$
(B) $(1-e)$
(C) $e$
(D) $e^{-1}$

Ankur S
Ankur S
Numerade Educator
01:07

Problem 150

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A=10 \mathrm{~cm}^{2}$ and length $=20 \mathrm{~cm} .$ If one of the solenoid has 300 turns and the other 400 turns, their mutual inductance is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}\right) \quad[\mathbf
(A) $2.4 \pi \times 10^{-5} \mathrm{H}$
(B) $4.8 \pi \times 10^{-4} \mathrm{H}$
(C) $4.8 \pi \times 10^{-5} \mathrm{H}$
(D) $2.4 \pi \times 10^{-4} \mathrm{H}$

Ankur S
Ankur S
Numerade Educator
02:10

Problem 151

An inductor of inductance $L=400 \mathrm{mH}$ and resistors of resistance $R_{1}=2 \Omega$ and $R_{2}=2 \Omega$ are connected to a battery of EMF $12 \mathrm{~V}$ as shown in Fig. $16.71$. The internal resistance of the battery is negligible. The switch $S$ is closed at $t=0 .$ The potential drop across $L$ as a function of time is
(A) $\frac{12}{t} e^{-3 t} \mathrm{~V}$
(B) $6\left(1-e^{-t / 0.2}\right) \mathrm{V}$
(C) $12 e^{-5 t} \mathrm{~V}$
(D) $6 e^{-5 t} \mathrm{~V}$

Ankur S
Ankur S
Numerade Educator
02:16

Problem 152

A rectangular loop has a sliding connector $P Q$ of length $\ell$ and resistance $R \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_{1}, I_{2}$, and $I$ are
(A) $I_{1}=-I_{2}=\frac{B l v}{6 R}, I=\frac{2 B l v}{6 R}$
(B) $I_{1}=I_{2}=\frac{B l v}{3 R}, I=\frac{2 B l v}{3 R}$
(C) $I_{1}=I_{2}=I=\frac{B l v}{R}$
(D) $I_{1}=I_{2}=\frac{B l v}{6 R}, I=\frac{B l v}{3 R}$

Ankur S
Ankur S
Numerade Educator
01:27

Problem 153

A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil, it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to
(A) development of air current when the plate is placed.
(B) induction of electrical charge on the plate.
(C) shielding of magnetic lines of force as aluminium is a paramagnetic material.
(D) electromagnetic induction in the aluminium plate giving rise to electromagnetic damping.

Ankur S
Ankur S
Numerade Educator
02:32

Problem 154

A circular loop of radius $0.3 \mathrm{~cm}$ lies parallel to a much bigger circular loop of radius $20 \mathrm{~cm}$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15 \mathrm{~cm}$. If a current of $2.0 \mathrm{~A}$ flows through the smaller loop, then the flux linked with bigger loop is
(A) $6 \times 10^{-11}$ weber
(B) $3.3 \times 10^{-11}$ weber
(C) $6.6 \times 10^{-9}$ weber
(D) $9.1 \times 10^{-11}$ weber

Ankur S
Ankur S
Numerade Educator
01:56

Problem 155

In the circuit shown here, the point $C$ is kept connected to point $A$ till the current flowing through the circuit becomes constant. Afterward, suddenly, point $C$ is disconnected from point $a$ and connected to point $B$ at time $t=0$. Ratio of the voltage across resistance and the inductor at $t=L / R$ will be equal to
(A) $\frac{e}{1-e}$
(B) 1
(C) $-1$
(D) $\frac{1-e}{e}$

Ankur S
Ankur S
Numerade Educator
02:25

Problem 156

An inductor $(L=0.03 \mathrm{H})$ and a resistor $(R=0.15 \mathrm{k} \Omega)$ are connected in series to a battery of $15 \mathrm{~V}$ EMF in a circuit shown below. The key $K_{1}$ has been kept closed for a long time. Then at $t=0, K_{1}$ is opened and key $K_{2}$ is closed simultaneously. At $t=1 \mathrm{~ms}$, the current in the circuit will be: $\left(e^{5} \cong 150\right.$ )
(A) $67 \mathrm{~mA}$
(B) $6.7 \mathrm{~mA}$
(C) $0.67 \mathrm{~mA}$
(D) $100 \mathrm{~mA}$

Ankur S
Ankur S
Numerade Educator
02:32

Problem 157

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit, the capacitor is charged to $Q_{0}$ and then connected to the $L$ and $R$ as shown below If a student plots graphs of the square of maximum charge $\left(Q_{\mathrm{Max}}^{2}\right)$ on the capacitor with time $(t)$ for two different values $L_{1}$ and $L_{2}\left(L_{1}>L_{2}\right)$ of $L$ then which of the following represents this graph correctly? (Plots as schematic and not drawn to scale)
(A)
(B)
(C)
(D)

Ankur S
Ankur S
Numerade Educator
02:12

Problem 158

An arc lamp requires a direct current of $10 \mathrm{~A}$ at $80 \mathrm{~V}$ to function. If it is connected to a $220 \mathrm{~V}$ (rms), and a $50 \mathrm{~Hz} \mathrm{AC}$ supply, the series inductor needed for it to work is close to
(A) $0.08 \mathrm{H}$
(B) $0.044 \mathrm{H}$
(C) $0.065 \mathrm{H}$
(D) $80 \mathrm{H}$

Ankur S
Ankur S
Numerade Educator