Final answer:
To make the total potential at the remaining empty corner of the square 0 V, a negative charge of -2 * 7.67μC / √2 should be placed at one of the empty corners.
Step-by-step explanation:
To determine the charge that should be fixed to one of the empty corners so that the total potential at the other empty corner is 0 V, we need to apply the principle of superposition for electric potentials. Since we have two identical +7.67 μC charges fixed at adjacent corners of a square, let's assume the side of the square is d. The electric potential due to a point charge is given by the formula V = k * Q / r, where k is Coulomb's constant, Q is the charge, and r is the distance from the charge to the point where potential is being calculated.
There are two contributions to the potential at the empty corner: the direct diagonal contribution from the charges V1 and V2, which are both k * 7.67μC / (√d * d). Since the potentials due to individual charges are additive, we have a total contribution from the two charges of 2V1. To make the total potential zero, we need to place a charge Q3 at one of the empty corners such that the potential it creates V3 cancels out the 2V1.
V3 must equal -2V1. Since V3 = k * Q3 / r and r in this case is equal to d, we can write k * Q3 / d = -2(k * 7.67μC / (√d * d)). Solving for Q3, we find that Q3 = -2 * 7.67μC / √2. The algebraic sign is negative, meaning that the charge must be negative to create an opposing electric potential that cancels out the positive potential.