Physics

Problem

Four identical point charges

+q

are fixed at the corners of a square whose side length is

a

. Which of the following numerical factors multiplies

kq^{2}/a

in the expression for the total electric potential energy of the system? a)

4

5

4+\sqrt{2}

6

Intuitive explanation

The key is recognizing that potential energy counts each pair interaction once. With four identical charges, you need to identify all unique pairs and calculate the potential energy for each: adjacent charges separated by $a$ , and diagonal charges separated by $a\sqrt{2}$ . Sum these contributions carefully—there are 4 edge pairs and 2 diagonal pairs—then express the total as a multiple of $kq^2/a$ .

Intuitive explanation

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