Continuous Charge Distribution

Answer the following question.

State the units of linear charge density.

(a) A conductor A with a cavity as shown in Fig (a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor.

(b) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig. (b)].

(c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

Two charges 5 μC and -4μC are kept 5.0 m apart at points A and B respectively. How much work will have to be done to move the charge at A through a distance of 5.0 m further away from point B along the line BA?

A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is `(sigma/(2in_0)) hat"n"`. where `hat"n"` is the unit vector in the outward normal direction, and `sigma` is the surface charge density near the hole.

An infinite line charge produces a field of 9 × 10⁴ N/C at a distance of 2 cm. Calculate the linear charge density.

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.7 × 10^–22 C/m². What is electric field intensity E:

1. in the outer region of the first plate, and
2. between the plates?