Two conducting plates X and Y , each having a large surface area A (on one side), are positioned parallel to one another. A charge Q is imparted to plate X , while the other plate remains neutral. Determine the electric field at a point to the right of the plates.

Step-by-step solution

Let the charges on the four surfaces of the two plates be Q₁, Q₂ (for plate X) and Q₃, Q₄ (for plate Y), starting from left to right. The total charge on plate X is Q , so Q₁ + Q₂ = Q . The total charge on plate Y is 0 , so Q₃ + Q₄ = 0 . The charges on the outermost surfaces of the two parallel plates are always equal and are given by half the sum of the total charges on the plates: Q₁ = Q₄ = Q_X + Q_Y 2 = Q + 0 2 = Q 2 The charges on the inner facing surfaces are: Q₂ = Q - Q₁ = Q - Q 2 = Q 2 Q₃ = 0 - Q₄ = - Q 2 Th