Concepts of Physics 2 for IIT JEE

H C Verma Harish Chandra Verma

Chapter 30 Gauss's Law - all with Video Answers

Educators

Chapter Questions

03:26

Problem 1

The electric field in a region is given by $\vec{E}=\frac{3}{5} E_{0} \vec{i}+\frac{4}{5} E_{0} \vec{j}$ with $E_{0}=2 \cdot 0 \times 10^{3} \mathrm{~N} \mathrm{C}^{-1}$. Find the flux
of this field through a rectangular surface of area $0-2 \mathrm{~m}^{2}$ parallel to the $y-z$ plane.

Sanu Kumar

Numerade Educator

03:02

Problem 2

A charge $Q$ is uniformly distributed over a rod of length $l$. Consider a hypothetical cube of edge $l$ with the centre of the cube at one end of the rod. Find the minimum possible flux of the electric field through the entire surface of the cube.

Dr. Rajveer Singh

Numerade Educator

04:51

Problem 3

Show that there can be no net charge in a region in which the electric field is uniform at all points.

Dr. Rajveer Singh

Numerade Educator

03:22

Problem 4

The electric field in a region is given by $\vec{E}=\frac{E_{0} x}{l} \vec{i} .$ Find the charge contained inside a cubical volume bounded by the surfaces $x=0, x=a, y=0, y=a, z=0$ and $z=a$. Take $E_{0}=5 \times 10^{3} \mathrm{~N} \mathrm{C}^{-1}, l=2 \mathrm{~cm}$ and $a=1 \mathrm{~cm}$.

Ajay Singhal

Numerade Educator

03:02

Problem 5

A charge $Q$ is placed at the centre of a cube. Find the flux of the electric field through the six surfaces of the cube.

Dr. Rajveer Singh

Numerade Educator

01:32

Problem 6

A charge $Q$ is placed at a distance $a / 2$ above the centre of a horizontal, square surface of edge $a$ as shown in figure (30-E1). Find the flux of the electric field through the square surface.

Mahipal Kumawat

Numerade Educator

02:52

Problem 7

Find the flux of the electric field through a spherical surface of radius $R$ due to a charge of $10^{-7} \mathrm{C}$ at the centre and another equal charge at a point $2 R$ away from the centre (figure $30-\mathrm{E} 2$ ).

Khoobchandra Agrawal

Numerade Educator

04:19

Problem 8

A charge $Q$ is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and the Gauss's law, find the flux of the electric field due to this charge through the surface of the hemisphere (figure $30-\mathrm{EB})$

Keshav Singh

Numerade Educator

04:39

Problem 9

A spherical volume contains a uniformly distributed charge of density $2.0 \times 10^{-4} \mathrm{C} \mathrm{m}^{-3}$. Find the electric field at a point inside the volume at a distance $4.0 \mathrm{~cm}$ from the centre.

Supratim Pal

Numerade Educator

03:23

Problem 10

The radius of a gold nucleus $(Z=79)$ is about $7.0 \times 10^{-15} \mathrm{~m} .$ Assume that the positive charge is distributed uniformly throughout the nuclear volume. Find the strength of the electric field at (a) the surface of the nucleus and (b) at the middle point of a radius. Remembering that gold is a conductor, is it justified to assume that the positive charge is uniformly distributed over the entire volume of the nucleus and does not come to the outer surface?

Ajay Singhal

Numerade Educator

05:00

Problem 11

A charge $Q$ is distributed uniformly within the material of a hollow sphere of inner and outer radii $r_{1}$ and $r_{2}$ (figure $30-\mathrm{E} 4$ ). Find the electric field at a point $P$ a distance $x$ away from the centre for $r_{1}<x<r_{2} .$ Draw a rough graph showing the electric field as a function of $x$ for $0<x<2 r_{2}$ (figure $30-\mathrm{E} 4$ ).

Rajesh Kumar

Numerade Educator

06:05

Problem 12

A charge $Q$ is placed at the centre of an uncharged, hollow metallic sphere of radius $a$.
(a) Find the surface charge density on the inner surface and on the outer surface.
(b) If a charge $q$ is put on the sphere, what would be the surface charge densities on the inner and the outer surfaces ?
(c) Find the electric field inside the sphere at a distance $x$ from the centre in the situations (a) and (b).

Susan Hallstrom

Numerade Educator

13:52

Problem 13

Consider the following very rough model of a beryllium atom. The nucleus has four protons and four neutrons confined to a small volume of radius $10^{-15} \mathrm{~m} .$ The two $1 s$ electrons make a spherical charge cloud at an average distance of $1.3 \times 10^{-11} \mathrm{~m}$ from the nucleus, whereas the two $2 s$ electrons make another spherical cloud at an average distance of $5 \cdot 2 \times 10^{-11} \mathrm{~m}$ from the nucleus. Find the electric field at (a) a point just inside the $1 s$ cloud and (b) a point just inside the $2 s$ cloud.

Linda Winkler

Numerade Educator

04:26

Problem 14

Find the magnitude of the electric field at a point $4 \mathrm{~cm}$ away from a line charge of density $2 \times 10^{-6} \mathrm{C} \mathrm{m}^{-1}$.

Bettina Hanlon

Numerade Educator

04:48

Problem 15

A long cylindrical wire carries a positive charge of linear density $2.0 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1}$. An electron revolves around it in a circular path under the influence of the attractive electrostatic force. Find the kinetic energy of the electron. Note that it is independent of the radius.

Ameer Said

Numerade Educator

05:40

Problem 16

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. Find the electric field at a point $P$ inside the cylindrical volume at a distance $x$ from its axis (figure $30-\mathrm{E} 5)$

Nathan Silvano

Numerade Educator

04:42

Problem 17

A nonconducting sheet of large surface area and thickness $d$ contains uniform charge distribution of density $\rho$. Find the electric field at a point $P$ inside the plate, at a distance $x$ from the central plane. Draw a qualitative graph of $E$ against $x$ for $0<x<d$.

Eduard Sanchez

Numerade Educator

01:00

Problem 18

A charged particle having a charge of $-2 \cdot 0 \times 10^{-6} \mathrm{C}$ is placed close to a nonconducting plate having a surface charge density $4 \cdot 0 \times 10^{-6} \mathrm{C} \mathrm{m}^{-2}$. Find the force of attraction between the particle and the plate.

Raj Bala

Numerade Educator

02:26

Problem 19

One end of a $10 \mathrm{~cm}$ long silk thread is fixed to a large vertical surface of a charged nonconducting plate and the other end is fastened to a small ball having a mass of $10 \mathrm{~g}$ and a charge of $4 \cdot 0 \times 10^{-6} \mathrm{C}$. In equilibrium, the thread makes an angle of $60^{\circ}$ with the vertical. Find the surface charge density on the plate.

Averell Hause

Carnegie Mellon University

08:17

Problem 20

Consider the situation of the previous problem. (a) Find the tension in the string in equilibrium. (b) Suppose the ball is slightly pushed aside and released. Find the time period of the small oscillations.

Ren Jie Tuieng

Numerade Educator

02:38

Problem 21

Two large conducting plates are placed parallel to each other with a separation of $2 \cdot 00 \mathrm{~cm}$ between them. An electron starting from rest near one of the plates reaches the other plate in $2 \cdot 00$ microseconds. Find the surface charge density on the inner surfaces.

Supratim Pal

Numerade Educator

00:47

Problem 22

Two large conducting plates are placed parallel to each other and they carry equal and opposite charges with surface density $\sigma$ as shown in figure $(30-\mathrm{E} 6) .$ Find the electric field (a) at the left of the plates, (b) in between the plates and (c) at the right of the plates.

Prem Bijarniya

Numerade Educator

04:00

Problem 23

Two conducting plates $X$ and $Y$, each having large surface area $A$ (on one side), are placed parallel to each other as shown in figure $(30-\mathrm{E} 7) .$ The plate $X$ is given a charge $Q$ whereas the other is neutral. Find (a) the surface charge density at the inner surface of the plate $X$, (b) the electric field at a point to the left of the plates,
(c) the electric field at a point in between the plates and (d) the electric field at a point to the right of the plates.

Mahendra Kumar

Numerade Educator

03:17

Problem 24

Three identical metal plates with large surface areas are kept parallel to each other as shown in figure (30-E8). The leftmost plate is given a charge $Q$, the rightmost a charge $-2 Q$ and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.

Mirza Aslam Beig

Numerade Educator