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

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

Permittivity of free space, ε₀ = 8.85 × 10⁻¹² C N⁻¹ m⁻²

As both plates have the same surface charge density σ.

`E_A = E_B = σ/(2ε_0)`

(a) In region-I,

• The field due to positive plate A is toward the left.
• The field due to negative plate B is toward the right.

So the fields oppose each other.

E_I = E_B − E_A 

= `σ/(2ε_0) - σ/(2ε_0)`

= 0

(b) In region-III,

• The field due to plate A is toward the right.
• The field due to plate B is toward the left.

Again, the fields oppose each other.

E_III = E_A − E_B 

= `σ/(2ε_0) - σ/(2ε_0)`

= 0

(c) In region-II,

• The field due to the positive plate is toward the right.
• The field due to the negative plate is also toward the right.

Hence, the fields add.

E_II = E_A + E_B 

= `σ/(2ε_0) + σ/(2ε_0)`

= `(σ + σ)/(2ε_0)`

= `(2σ)/(2ε_0)`

= ` σ/ε_0`

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

= 1.92 × 10⁻¹⁰ N/C