To determine the electric potential at the center of the square due to the four charges, we need to consider the contributions from each charge and then sum them up.
Given that each charge has a magnitude of +2 μC, we can calculate the electric potential due to a single point charge using the formula:
V = k * (q / r)
where V is the electric potential, k is the electrostatic constant (approximately 9 × 10^9 N m^2/C^2), q is the charge, and r is the distance from the charge to the point where we want to calculate the potential.
Since the square is symmetric, the charges are equidistant from the center. Let's assume the distance from the center to each corner of the square is represented by 'd'. In this case, the distance from the center to each charge is also 'd'.
The electric potential at the center due to a single charge is:
V1 = k * (q / d)
Since all four charges are identical, the total potential at the center will be the sum of the potentials due to each charge:
V_total = V1 + V1 + V1 + V1 = 4 * V1
Substituting the values:
V_total = 4 * (k * (q / d))
Now we can plug in the known values:
k ≈ 9 × 10^9 N m^2/C^2 q = 2 μC = 2 × 10^(-6) C d = 30 cm = 0.3 m
V_total = 4 * (9 × 10^9 N m^2/C^2) * (2 × 10^(-6) C) / 0.3 m
Calculating this expression gives the electric potential at the center of the square due to the four charges.