24.6 : Calculations of Electric Potential I

Consider a spherical conductor with a radius of 20 centimeters and a charge of 40 micro-coulombs. What would be the electric potential at radial distances of 60 and 10 centimeters?

According to Gauss's law, the electric field inside the sphere is zero. So, to move a test charge within the sphere no work is done. The electric potential is constant inside the sphere and its value is the same as the potential at the surface.

Outside the sphere, the electric field follows the inverse square law. The electric potential is the integral of the dot product of the electric field and the displacement. At an infinite distance, the potential is defined as zero. This gives potential which varies inversely with the radial distance.

So, the electric potential is continuous, but the electric field is discontinuous.

Here, the known quantities are the sphere's radius, epsilon zero, and the charge. The unknown quantities are the electric potential at the two distances. By substituting the known quantities, the potential at 60 centimeters and at 10 centimeters are calculated.