A hollow metal sphere of radius is charged such that the potential on its surface is The potential at the center of the sphere is
Step 1. Given data
The potential on the surface
The radius of the sphere
Step 2. Formula used
Potential is given as,
Where is the charge and is the permeability and is the radius
Step 3. Find the potential at the center of the sphere
The sphere is hollow and made of metal and it can conduct electricity. We know that there is no electric field inside the hollow sphere.
Since the electric field is zero inside the sphere, the potential will be same everywhere inside the sphere. Given electric potential is Thus the potential at the center is
Hence, the potential at the centre of the sphere is
Note:
Let re the radius of the sphere the electric field and the potential, is the charge
if the electric field will be zero for metallic charged sphere.
if the potential will be constant throughout the metallic charged sphere.