Question

Two conducting plates X and Y, each having large surface area A (on one side), are placed parallel to each other as shown in figure (30-E7). The plate X is given. a charge Q whereas the other is neutral. Find (a) the -surface charge density at the inner surface of the plate X, (b) the electric field at a point to the left of the plates, (c) the electric field at a point in between the plates and (d) the electric field at a point to the right of the plates.

Answer 1

(a) For the surface charge density of a single plate.

Let the surface charge density at both sides be σ₁ & σ₂

(b) Electric field to the left of the plates = σ/ ε₀

Since σ = Q/2A 

Hence Electricfield = Q/2Aε₀ 

This must be directed toward left as ‘X’ is the charged plate. 

(c) & (d) Here in both the cases the charged plate ‘X’ acts as the only source of electric field, with (+ve) in the inner side and ‘Y’ attracts towards it with (-ve) he in its inner side. So for the middle portion E = Q/2Aε₀  towards right. 

(d) Similarly for extreme right the outerside of the ‘Y’ plate acts as positive and hence it repels to the right with E = Q/2Aε₀