Question

If a charged conducting shell has potential V at its centre. What is electric potential at a point 30 cm from its surface, radius of shell is 10 cm
3V

2V

v/4
v/2

Answer 1

Given:

A charged conducting shell has potential V at its centre. Radius of shell is 10 cm.

To find:

Electric potential at 30 cm from centre?

Calculation:

• In case of a charged shell, the electric potential at the centre is equal to the electric potential at the surface ( i.e. potential remains constant inside the shell).

$\rm \: V_{centre} = V_{surface}$

$\rm \implies \: \dfrac{kq}{r} = V$

• Putting r = 10 cm.

$\rm \implies \: \dfrac{kq}{10} = V$

Now, when we consider a distance R > r (radius of shell), the potential equation becomes:

$\rm \: V_{outside} = \dfrac{kq}{R}$

• R = 30 + 10 = 40 cm.

$\rm \implies\: V_{outside} = \dfrac{kq}{40}$

$\rm \implies\: V_{outside} = \dfrac{1}{4} \times \dfrac{kq}{10}$

$\rm \implies\: V_{outside} = \dfrac{V}{4}$

So, at the required distance, potential is V/4 (OPTION 3).