Question

Part A A conducting sphere is charged up such that the potential on its surface is 100 V (relative to infinity). If the sphere's radius were twice as large, but the charge on the sphere were the same, what would be the potential on the surface relative to infinity?

Answer 1

Answer:

$V_{2}=\frac{V_{1}}{2}$    

Explanation:

The potential of a conducting sphere is the same as a punctual charge,

First sphere:

$V_{1}=k*q_{1}/r_{1}$    (1)

Second sphere:

$V_{2}=k*q_{2}/r_{2}$        (2)

But, second sphere's radius is twice first sphere radius, and their charges the same:

$q_{1}=q_{2}$

$r_{2}=2*r_{1}$

If we divide the equations (1) and (2), to solve V2:

$V_{2}=V_{1}*r_{1}/r_{2}=V_{1}/2$