Question
A hollow metal sphere of radius $$10\,cm$$ is charged such that the potential on its surface is $$80\,V.$$ The potential at the centre of the sphere is
A.
zero
B.
$$80\,V$$
C.
$$800\,V$$
D.
$$8\,V$$
Answer :
$$80\,V$$
Solution :
In case of spherical metal conductor hollow or solid for an internal point (i.e. $$r < R$$ ) potential everywhere inside is same. It is maximum at the surface of sphere and further going out of sphere its value decreases.
So, according to above graph
$$\eqalign{ & {V_{{\text{in}}}} = {V_{{\text{centre}}}} = {V_{{\text{surface}}}} \cr & = \frac{1}{{4\pi {\varepsilon _0}}} \times \frac{q}{R} = 80\,V\,\,\left[ {\because {V_{{\text{surface}}}} = 80\,V} \right] \cr} $$
In case of spherical metal conductor hollow or solid for an internal point (i.e. $$r < R$$ ) potential everywhere inside is same. It is maximum at the surface of sphere and further going out of sphere its value decreases.
So, according to above graph
$$\eqalign{ & {V_{{\text{in}}}} = {V_{{\text{centre}}}} = {V_{{\text{surface}}}} \cr & = \frac{1}{{4\pi {\varepsilon _0}}} \times \frac{q}{R} = 80\,V\,\,\left[ {\because {V_{{\text{surface}}}} = 80\,V} \right] \cr} $$