Question

An isolated conductor of arbitrary shape has a net charge of +1.1 10-5 C. Inside the conductor is a cavity within which is a point charge q = +3.4 10-6 C.
(a) What is the charge on the cavity wall?
1 . C

(b) What is the charge on the outer surface of the conductor?

Answer 1

Concepts and reason

The concepts used to solve this question is the charge by induction and conductors in electrostatic equilibrium.

Initially, use the concept of charge by induction to determine the charge on the cavity wall. Later determine the charge on the outer surface of the conductor by using the given values of the net charge of the conductor.

Fundamentals

Induction:

Induction is defined as the process in which the charge moves from one substance to another substance without physically touching each other. The charges move from one substance to another because lie charges repel and the unlike charges attract.

Electrostatic equilibrium:

In electrostatic equilibrium, the net electric field inside the conductor is zero because the net charge enclosed inside the conductor is zero. All the charge residing on the surface of the conductor in electrostatic equilibrium.

(a)

The net charge inside the isolated conductor is zero and therefore the charge on the cavity wall will be the same as that of charge within the cavity but the charge will be an opposite sign.

Hence, the charge on the cavity wall will be,

$q = - 3.4 \times {10^{ - 6}}{\rm{ C}}$

(b)

In electrostatic equilibrium, all the charge residing on the surface of the conductor.

Therefore the net charge on the surface of the conductor is,

$\begin{array}{c}\\Q = 1.1 \times {10^{ - 5}}{\rm{ C}} + 3.4 \times {10^{ - 6}}{\rm{ C}}\\\\ = 1.44 \times {10^{ - 5}}{\rm{ C}}\\\end{array}$

Ans: Part a

The charge on the cavity wall is $- 3.4 \times {10^{ - 6}}{\rm{ C}}$ .