Electric Potential due to Charged Non-conducting Sphere:
Consider a non-conducting sphere of radius R be charged by a charge q. The electric field intensity at the points outside the sphere, on the surface and inside the sphere is as follows:
The potential at a point in electric field intensity \(\vec E\) is calculated by the help of following relation
\(-\int_{\infty}^{r} \vec{E} \cdot \vec{d} r\)
The electric potential is calculated at the observation point in different conditions :
(a) At a point outside the non-conducting sphere
(b) At a point on the surface of non-conducting sphere
Putting r = R in equation (1),
VS = \(\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{R}\) ……………. (2)
(c) At a point inside the non-conducting sphere (r < R)
For a point inside the non-conducting sphere, the electric field intensity E does not depend uniformly from infinity to r distance, i.e., from infinity to surface, it is inversely proportional to the square of the distance r and it is directly proportional to the distance from the surface to the centre r. Thus, integral is divided into two parts:
For a point at centre, putting r = 0 in eqn. (3)
Thus, the electric potential at centre of a charged non-conducting sphere is 1.5 times that on its surface.
It is clear that the electric potential decreases with r2 from centre to surface in a charged non-conducting sphere. After that, it decreases as per the law of r-1 and becomes zero at infinity. It is shown in a graph in figure
