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 plates from left to right be q₁ , q₂ , q₃ , and q₄ . 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 electric field at any point is the vector sum of the fields produced by each of the four surface charge layers. Each surface acts as an infinite sheet of charge, producing a uniform electric field of magnitude 2 ₀ = q 2A ₀ . For a point to the left of both plates, the electric field due to each surface charge poin