Question

A charge Q is supplied to a metallic conductor. Which is true?(a) Electric field inside it is same as on the surface.
(b) Electric potential inside is zero.
(c) Electric potential on the surface is zero
(d) Electric potential inside it is constant

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Answer 1

Given:

A charge Q is supplied to a metallic conductor.

To find:

Correct statement among the following:

(a) Electric field inside it is same as on the surface.

(b) Electric potential inside is zero.

(c) Electric potential on the surface is zero

(d) Electric potential inside it is constant.

Calculation:

Let radius of sphere R

Applying Gauss' Theorem at a distance r from centre such r < R ;

$\therefore \: \displaystyle \: \int \: E \: . \: ds = \frac{Q_{enclosed} }{ \epsilon_{0}}$

Now , inside the conductor , the enclosed charge is zero ;

$= > \: \displaystyle \: \: E \: \int\: ds = \frac{Q_{enclosed} }{ \epsilon_{0}}$

$= > \: \displaystyle \: \: E \: \int\: ds = \frac{0 }{ \epsilon_{0}}$

$= > \: \displaystyle \: \: E \: \int\: ds = 0$

$= > \: \: \: E \: = 0$

So, field intensity inside conductor is zero.

Let potential difference at that point from centre be dV;

$\displaystyle \: \int \: dV = \int E \: dr$

$= > \displaystyle \: \int \: dV = \int 0 \times dr$

$= > \displaystyle \: \int \: dV =0$

$= > \:V_{2}-V_{1} =0$

$= > \:V_{2} = V_{1}$

So, potential inside conductor remains constant.

So, final answer is :

$\boxed{\sf{Option \: d}}$

Answer 2

Answer:

option d is correct

d) Electric potential inside it is constant