Answer: the answer is (b) 134.85 V.
Explanation:To calculate the potential at the center of the hexagon, we can use the formula:
V=kq/r
where V is the potential, k is the Coulomb constant (9 x 10^9 Nm^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 hexagon has six charges of 5 µC each, the total charge at the center is 6 * 5 µC = 30 µC.
To calculate the distance from the center to each of the charges, we can divide the hexagon into six congruent equilateral triangles, each with side 10 cm. The distance from the center to each vertex is the apothem of the hexagon, which can be calculated as:
a = 10 * sqrt(3) / 2
So the distance from the center to each charge is r = a = 10 * sqrt(3) / 2.
Now we can calculate the potential at the center of the hexagon as:
V = kq/r = (9 x 10^9 Nm^2/C^2) * (30 x 10^-6 C) / (10 * sqrt(3) / 2) = 134.85 V
