Understanding Electric Potential: Point Charges Arranged in a Circle

What is the electric potential at the center of a circle with five symmetrically placed identical point charges?

a) It is half the potential due to one charge.
b) It is five times the potential due to one charge.
c) It is the same as the potential due to one charge.
d) It is double the potential due to one charge.

Answer:

The correct answer is b) It is five times the potential due to one charge.

When five identical point charges are arranged symmetrically in a circle of radius R, each with charge q, the electric potential at the center is five times the potential due to one charge.

This can be calculated using the principle of superposition, where the electric potential due to each individual charge at the center is V = kq/R. Since the charges are symmetrically placed, their potentials at the center add up, resulting in a total electric potential of Vtotal = 5(kq/R).

This means that the electric potential at the center of a circle surrounded by five identical point charges is significantly higher than the potential due to a single charge. Understanding how charges interact and contribute to the overall electric potential is essential in studying the behavior of electric fields and their effects on surrounding objects.