Question

A hollow metal sphere of radius $10cm$ is charged such that the potential on its surface is $80volt.$ The potential at the center of the sphere is

Answer 1

Step 1. Given data

Potential on the surface $V$$=80volt.$

The radius of the sphere $r=10cm$

Step 2. Formula used

Potential $V$$=\frac{1}{4\pi {\epsilon }_0}·\frac{q}{r}$

Where $q$ is the charge and ${\mathrm{\epsilon }}_0$ is the permittivity and $r$ is the radius,

Step 3. Find the potential at the center of the sphere

1. The sphere is hollow and made of metal.
2. Thus it can conduct electricity.
3. We know that there is no electric field inside the hollow sphere.
4. Electric potential is defined as the work done per unit coulomb against the electric field to move the charge from a reference point to a measuring point
5. Given electric potential is $80volt.$
6. Since the electric field is zero inside the sphere, the potential will be the same everywhere inside the sphere.
7. Thus the potential at the center is $80volt.$

Hence, the potential at the center of the sphere is $80volt.$

Note:-

Let $R$ re the radius of the sphere $E$ the electric field and $P$ the potential, $Q$ is the charge

$E=\frac{1}{4\pi {\epsilon }_0}·\frac{Q}{r^2},r>R$if $r<R$ the electric field will be zero for the metallic charged sphere

$V=\frac{1}{4\pi {\epsilon }_0}·\frac{Q}{r},r>R$if $r<R$ the potential will be constant throughout the metallic charged sphere