Identical 2.0-$\mu$C charges are located on the vertices of a square with sides that are 2.0 m in length.Determine the electric potential (relative to zero at infinity)at the center of the square.
A)38 kV
B)51 kV
C)76 kV
D)64 kV
E)13 kV

Question

Quizplus · Accepted Answer

The electric potential at the center of the square can be calculated by summing the contributions from each charge:
V = kq/r1 + kq/r2 + kq/r3 + kq/r4
where q is the charge, r1-r4 are the distances from each charge to the center of the square, and k is the Coulomb constant.
In this case, since the charges are identical and arranged symmetrically, r1 = r3 and r2 = r4, so the equation simplifies to:
V = kq/r1 + kq/r2 + kq/r1 + kq/r2
V = 2kq/r1 + 2kq/r2
The distance from each charge to the center of the square is d/√2, where d is the length of the side of the square. Therefore:
r1 = r2 = d/√2
Substituting this into the equation for V:
V = 2kq/d*√2
V = 2(9×10^9 N·m^2/C^2)(2×10^-6 C) / (2 m/√2)
V ≈ 51 kV 
Therefore, the best choice is B.

Identical 2 μ\muμ C Charges Are Located on the Vertices of a Square

Identical 2 $\mu$ C Charges Are Located on the Vertices of a Square