Four charges of Q = 10 nC sit at the four corners of a square with 10 cm sides. How much energy is required to bring a charge q = 1.0 nC from very far away to the exact center of the square?

1. The distance from the center of a 10 cm square to each corner is half the diagonal: (0.10 m)(sqrt(2)) / 2 = 0.0707 m. 2. Each of the four identical corner charges contributes the same potential at the center: k Q / r = (8.99 x 10^9)(10 x 10^-9) / 0.0707 = 1271 V. 3. Four equal corner charges give a total potential of 4 x 1271 V = 5086 V at the center. 4. The energy needed to bring q = 1.0 nC in from infinity is U = qV = (1.0 x 10^-9 C)(5086 V) = 5.1 x 10^-6 J. 5. Option C uses the distance to a corner as if it were the full side length rather than the shorter distance to the center, which understates the potential. _Source: OpenStax Physics (CC BY 4.0), Ch 18 "Static Electricity", section 18.4 Electric Potential_