Question

Two concentric metallic shell have radii 10 cm and 20 cm. the outer shell is given a positive charge 5 μc and the inner shell is earthed. what is the charge on the inner shell

Answer 1

See diagram enclosed.

Given q1 = 5μC. r1 = 10 cm. r2 = 20 cm.

The inner metallic shell is earthed. So its Electrostatic potential is always zero. But due to charge q1 on the outer shell the potential becomes positive.

So some negative charge flows from the Earth to its surface to make the net potential equal to 0.

K = 1/(4 Pi epsilon)

Potential inside a hollow sphere is equal to that at the surface.

Net sum of the Potentials on the inner shell
= V = K q1 / r1 - K q2 / r2
= 0 (earthed).

So q2 = q1 * r2 / r1
Or, q2 = 5 * 10 / 20 = 2.5 μC.

Net Charge on inner hollow sphere = - 2.5 μC

Answer 2

Refer to the attachment for diagram

Given, Q1 = 5 μc.

R1 = 20cm , R2 = 10cm

Here, potential on inner shell is zero

but due to Q1,the potential rises,so some negative charge comes on Q2 from earth to make the net potential zero.

Now,

let K = 1/ 4πEo

Net potential in inner shell will be=>

V = (Q1×k)/R1 + (Q2 ×k)/R2 =0

=>Q2 = -2.5μc.

Hence the charge on the inner shell will be 2.5μc.