Question

Three large non conducting plane sheets of charge with charge densities

Answer 1

Radius = a

Explanation:

The question is incomplete. However, the question is about the relations between radius and aperture.

Electric field intensity  at a distance r from the plate = σ/2ε * (1 - r/root of a^2+r^2)

Carved portion is removed, so we replace σ = -σ.

We get -σ/2ε * (1 - r/root of a^2+r^2)

Effective electric intensity = σ/2ε + -σ/2ε * (1 - r/root of a^2+r^2)  

σr * (1 - r/root of a^2+r^2) = σ/2ε * (1/root of 2)

So r= a.