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

Part a)

`Q = 4\pi \epsilon_0 r V`

Part b)

`\sigma = (\epsilon_0 V)/(r)`

Step-by-step explanation:

Part a)

As we know that potential of the sphere is given as

`V = (kQ)/(r)`

`V = (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 = (Q)/(4\pi r^2)`

now we have

`\sigma = (4\pi \epsilon_0 r V)/(4\pi r^2)`

`\sigma = (\epsilon_0 V)/(r)`