As shown in the figure, three identical metal plates having large surface areas are positioned parallel to one another. A charge Q is given to the leftmost plate, a charge -2Q is given to the rightmost plate, and the middle plate is left neutral. Determine the charge that appears on the outer surface of the rightmost plate.

Step-by-step solution

Let the charges on the three plates from left to right be Q₁ = Q , Q₂ = 0 , and Q₃ = -2Q . The total charge on the system of plates is: Q_ total = Q₁ + Q₂ + Q₃ = Q + 0 - 2Q = -Q For a system of parallel conducting plates, the charge appearing on the outermost surfaces of the leftmost and rightmost plates is always equal and is exactly half of the total charge of the system. This is a direct consequence of Gauss's law and the fact that the electric field inside the bulk of the conducting plates must be zero. Let q_