Question

What are (a) the charge and (b) the charge density on the surface of a conducting sphere of radius r whose potential is V (with V = 0 at infinity)? State your answers in terms of the given variables, using ε0 if necessary.

Answer 1

Answer:

Part a)

$Q = 4\pi \epsilon_0 r V$

Part b)

$\sigma = \frac{\epsilon_0 V}{r}$

Explanation:

Part a)

As we know that potential of the sphere is given as

$V = \frac{kQ}{r}$

$V = \frac{Q}{4\pi \epsilon_0 r}$

now we have

$Q = 4\pi \epsilon_0 r V$

Part b)

Now we know that for conducting charged sphere whole charge is distributed over the surface of the sphere

so we will have

$\sigma = \frac{Q}{4\pi r^2}$

now we have

$\sigma = \frac{4\pi \epsilon_0 r V}{4\pi r^2}$

$\sigma = \frac{\epsilon_0 V}{r}$