Question

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 17.0 × 10⁻²² C/m2. What is E:

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

Answer 1

The situation is represented in the following figure.

A and B are two parallel plates close to each other. Outer region of plate A is labelled as I, the outer region of plate B is labelled as III, and the region between the plates, A and B, is labelled as II.

Charge density of plate A, σ = 17.0 × 10⁻²² C/m²

Charge density of plate B, σ = −17.0 × 10⁻²² C/m²

In regions, I and III, electric field E is zero. This is because the charge is not enclosed by the respective plates.

Electric field E in region II is given by the relation,

`"E" = sigma/in_0`

Where,

∈₀ = Permittivity of free space = 8.854 × 10⁻¹² N⁻¹ C² m⁻²

∴ `"E" = (17.0 xx 10^-22)/(8.854 xx 10^-12)`

= 1.92 × 10⁻¹⁰ N/C

Therefore, the electric field between the plates is 1.92 × 10⁻¹⁰ N/C.