Question

Two large, thin metal plates are parallel and close to each other. Ontheir inner faces, the plates have surface charge densities of oppositesigns and of magnitude 17.0 × 10–22 C/m2. What is E: (a) in the outerregion of the first plate, (b) in the outer region of the second plate,and (c) between the plates?

Answer 1

Given: The magnitude of surface charge density on the inner faces of the plates is 17× 10 −22  C/ m 2 .

a)

An arrangement of two parallel plates with uniform surface charge density is shown below.

The figure shows the two plates, plate A and plate B are placed parallel to each other. Region I and region III are the outer region of the plate and region II is the inner region of the plate.

Let σ A and σ B be the charge density of the plate A and plate B respectively and the charge density on plate A is positive.

Here,

σ A =17× 10 −22  C/ m 2 σ B =−17× 10 −22  C/ m 2

In the outer region of plate A that is region I, there is no charge enclosed by plate A.

Thus, the intensity of electric field is zero in the outer region of plate A.

b)

In the outer region of plate B that is region III, there is no charge enclosed by plate B.

Thus, the intensity of electric field is zero in the outer region of plate B.

c)

The electric field in the region II is given as,

E= σ ε 0

Where, the surface charge density is σ.

The ε 0 be the permittivity of free space,

ε 0 =8.854× 10 −12   C 2 / Nm 2

By substituting the given values in the above equation, we get

E= 17× 10 −22 8.854× 10 −12 =1.92× 10 −10  N/C

Thus, the magnitude of electric field between the plates is 1.92× 10 −10  N/C .