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

Answer 1

Electric Potential inside it is constant (Option d)

• First of all, charge Q is given to the surface of a spherical conducting shell.

As per GAUSS' LAW :

$\displaystyle \oint E \times ds = \frac{q}{ \epsilon_{0} }$

• 'q' refers to enclosed charge.

• Now, inside the conductor, the enclosed charge is zero, because all charge is on the surface.

$\implies \displaystyle \oint E \times ds = \frac{0}{ \epsilon_{0} }$

$\implies E = 0$

Now, we know the relation between electric field intensity and potential as :

• $\boxed{E = \dfrac{dV}{dr}}$

$\implies \dfrac{dV}{dr} = 0$

$\implies dV = 0$

$\implies V = constant$

So, electric potential is constant inside conductor. OPTION d) ✔️