Question

2. किसी आवेशित गोलीय कवच के आन्तरिक बिन्दु पर विद्युत विभव का
मान होता है। (The electric potential at a point inside a charged
spherical shell is)
V
(A) शून्य (Zero)
R) स्थिर (Constant)
(C) परिवर्ती (Variable)
(D) महत्तम (Maximum) ​

Answer 1

Given:

A charged spherical shell is provided.

To find:

The electric potential inside it ?

Calculation:

First of all, you should know that the electrostatic field intensity inside the charged sphere is zero.

At a distance r < R from centre :

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

Putting the limits :

$\implies \displaystyle \: \int_{V_{s}}^{V} \: dV = - \int_{R}^{r} E \: dr$

$\implies \displaystyle \: \int_{V}^{V_{s}} \: dV = \int_{R}^{r} E \: dr$

$\implies \displaystyle \: V_{s} -V = \int_{R}^{r} 0 \times \: dr$

$\implies \displaystyle \: V_{s} -V = 0$

$\implies \displaystyle \:V = V_{s}$

$\implies \displaystyle \:V = \frac{q}{4\pi \epsilon_{0}R}$

$\implies \displaystyle \:V = constant$

So, potential inside the sphere is constant .