Question

The potential at the center of a 4.0-cm-diameter copper sphere is 500 V, relative to V = 0 V at infinity. How much excess charge is on the sphere?

Short answer

The excess charge is on the sphere is 1.1nC .

Step-by-step solution

Given Information

We have given that the potential at the center of a 4.0-cm-diameter copper sphere is 500 V, relative to V = 0 V at infinity.

Simplify

The sphere is conductive, the potential will be the same throughout the volume, and will be equal to the potential at the surface of the sphere. The potential created by charge

$V=\frac{kq}{r}$,

Where r is the given radius of the sphere. and solve for the charge as

localid="1648562464911" $q=\frac{Vr}{k},$

Substituting radius with diameter

$q=\frac{Vd}{2k}$

Using the numerical values

localid="1649261072160" $q=\frac{500·0.04}{2·9·{10}^9}=1.1nC$