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

Consider the surfaces of the plates as 1, 2 (for plate X) and 3, 4 (for plate Y) from left to right. The total charge on the system of plates is Q_ net = Q + 0 = Q . The charge on the outermost surfaces (1 and 4) is equal to half of the total charge: q₁ = q₄ = Q_ net 2 = Q 2 The charges on the inner surfaces (2 and 3) are equal and opposite: q₂ = Q - q₁ = Q 2 q₃ = 0 - q₄ = - Q 2 The electric field at a point to the right of the plates is the vector sum of the fields due to all four surfaces. Taking the right direct