EASY

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In the shown figure a hemisphere is placed and two charges $3 q$ and $9 q$ are placed symmetrically about centre $O .$ Net electric flux over curved surface is given as $\frac{N_{1} q}{N_{2} ε_{0}},$ where $N_{1}$ and $N_{2}$ are lowest possible integers then value of $N_{1} + N_{2}$ is :

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Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

A conducting sphere of radius

R

is given a charge

Q .

The electric potential and the electric field at the center of the sphere respectively are:

HARD

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

The potential (in volts) of a charge distribution is given by

V (z) = 30 - 5 z^{2}

for

|z| \leq 1 m

V (z) = 35 - 10 |z|

for

|z| \geq 1 m

V (z)

does not depend on x and y. If this potential is generated by a constant charge per unit volume

ρ_{0}

(in units of

ϵ_{0}

) which is spread over a certain region, then choose the correct statement.

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

An electric field

\vec{E} = [4 x \hat{i} - (y^{2} + 1) \hat{j}] N C^{- 1}

passes through the box shown in figure. The flux of the electric field through surfaces

A B C D

and

B C G F

are marked as

ϕ_{I}

and

ϕ_{I I}

respectively. The value of

|ϕ_{I} - ϕ_{I I}|

is (in

N m^{2} C^{- 1}

) ____________.
Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

Consider the force

F

on a charge '

q

' due to a uniformly charged spherical shell of radius

R

carrying charge

Q

distributed uniformly over it. Which one of the following statements is true for

F

, if '

q

' is placed at distance

r

from the centre of the shell?

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

Four closed surfaces and corresponding charge distributions are shown below.

Question Image

Let the respective electric fluxes through the surfaces be

ϕ_{1}, ϕ_{2}, ϕ_{3}

and

ϕ_{4}

. Then:

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

The electric flux (in

SI

units) through any face of a cube due to a positive charge

Q

situated at the centre of a cube is

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

A hollow metal sphere of radius

R

is uniformly charged. The electric field due to the sphere at a distance

r

from the center

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

The number of electric lines that emerge from a finite charge

+ q

is _____

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

The magnitude of the average electric field normally present in the atmosphere just above the surface of the Earth is about

150 N / C

, directed inward towards the center of the Earth. This gives the total net surface charge carried by the Earth to be : [Given :

\in_{O} = 8.85 \times 1 0^{- 12} C^{2} / {N-m}^{2}, R_{E} = 6.37 \times 1 0^{6} m

]

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

The electric field in a region of space is given by,

\vec{E} = E_{0} \hat{i} + 2 E_{0} \hat{j}

where

E_{0} = 100 N C^{- 1}

. The flux of this field through a circular surface of radius

0.02 m

parallel to the

Y ‐ Z

plane is nearly

HARD

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

A circular disc of radius

R

carries surface charge density

σ (r) = σ_{0} (1 - \frac{r}{R})

, where

σ_{0}

is a constant and

r

is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is

ϕ_{0}

. Electric flux through another spherical surface of radius

\frac{R}{4}

and concentric with the disc is

ϕ

. Then the ratio

\frac{ϕ_{0}}{ϕ}

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

If some charge is given to a solid metallic sphere, the field inside remains zero and by Gauss's law all the charge resides on the surface. Suppose now that Colomb's force between two charges varies as

\frac{1}{r^{3}} .

Then, for a charged solid metallic sphere

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

In the following figures, which figure represents the variation of the electric field with distance from the centre of a uniformly charged non-conducting spheres of radius

R

HARD

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

In finding the electric field using Gauss law the formula

|\vec{E}| = \frac{q_{e n c}}{ε_{0} |A|}

is applicable. In the formula

ε_{0}

is permittivity of free space,

A

is the area of Gaussian surface and

q_{e n c}

is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

A point charge $q$ is placed at the corner of a cube of side $a$ as shown in the figure. What is the electric flux through the face $A B C D$ ?

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length $a$ as shown in the figure. A charge $+ Q$ is placed at the centre $O$ of the cube. $P$ is such a point outside the cube that the line $O P$ perpendicularly intersects the surface $A B C D$ at $R$ and also $O R = R P = a / 2$ . A charge $+ Q$ is placed at point $P$ also. What is the total electric flux through the five faces of the cube other than $A B C D ?$

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

Two hollow concentric spheres

A

and

B

are enclosing electric charges

2 C

and

8 C

respectively. If the radius of

A

is less than that of

B,

the ratio of electric flux through

A

to the electric flux through

B

HARD

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density

ρ = \frac{A}{r}

, where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

A charged particle moves with a velocity

v

in a circular path of radius

R

around a long uniformly charged conductor, then

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’ Law and Its Applications

Shown in the figure are two point charges

+ Q

and

- Q

inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If

σ_{1}

is the surface charge on the inner surface and

Q_{1}

net charge on it and

σ_{2}

the surface charge on the outer surface and

Q_{2}

net charge on it then:

Question Image

In the shown figure a hemisphere is placed and two charges 3q and 9q are placed symmetrically about centre O. Net electric flux over curved surface is given as N1qN2ε0, where N1 and N2 are lowest possible integers then value of N1+N2 is :

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

In the shown figure a hemisphere is placed and two charges $3 q$ and $9 q$ are placed symmetrically about centre $O .$ Net electric flux over curved surface is given as $\frac{N_{1} q}{N_{2} ε_{0}},$ where $N_{1}$ and $N_{2}$ are lowest possible integers then value of $N_{1} + N_{2}$ is :