Electric Potential due to Charged Spherical Shell:
(a) At point P outside the shell (r > R)
When unit positive test charge is brought from infinity to point P, then the potential at P is equal to negative value of line integral of electric field between infinity and P.
Therefore, according to definition of potential
(b) On the surface of the charged spherical shell (r = R)
According to the definition of potential,
Where V is constant
(c) Inside the charged spherical shell (r < R)
According to the definition of potential
Dependence of electric field upon distance is different e.g. outside spherical shell
E = \(\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}} \hat{r}\)
and inside the shell E = 0.
Therefore the integration can be written as under,
