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What do you mean by gauss theorem, and it's derivation

Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss' Law

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

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

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

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

Four closed surfaces and corresponding charge distributions are shown below.

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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

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

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

The number of electric lines that emerge from a finite charge

+ q

is _____

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss' Law

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

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

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

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

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

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

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

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

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

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

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

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

What do you mean by gauss theorem, and it's derivation

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

What do you mean by gauss theorem, and it's derivation