Question

a) What can you say about the charge density inside a piece of conducting material at electrostatic equilibrium? Justify your answer.

b) Explain why two distinct equipotential surfaces cannot intersect.

c) Explain why equipotential surfaces are perpendicular to the electric field lines.

d) A point charge q=30nC is placed in the cavity of a conducting shell. The shell itself has a total charge of -50nC. Find the charges on the inner and outer surfaces of the shell.

Answer 1

Here,

a) at the equilibrium

as the eelectric field inside the conducting material is zero

the charge desnity inside the conducting material is zero

b)

when two equipotential surfaces intersect , the potential on both the surfaces will be same at the point of intersection.

hence ,the equipotential will be same.

c)

as work done by electric field in moving the charge on an equipotential surface will be zero.

hence ,the electric field must be zero in the direction of motion

therefore , the equipotential surfaces are perpendicular to the electric field lines.

d)

charge on the inner surface = - charge on the point charge

charge on the inner surface = - 30 nC

charge on the inner surface is -30 nC

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charge on the outer surface = - 50 nC -(-30 nC)

charge on the outer surface = -20 nC