Three point charges +q, –2q and +q are placed along x-axis at point...

Question

Three point charges +q, –2q and +q are placed along x-axis at points x = –1 m, x = 0 m and x = 2 m respectively. The potential energy of the system is

Accepted Answer

Charges: $+q$ at $x=-1$, $-2q$ at $x=0$, $+q$ at $x=2$.

Distances: $r_{12}=1$ m, $r_{23}=2$ m, $r_{13}=3$ m.

$$U=k\left[\frac{(q)(-2q)}{1}+\frac{(-2q)(q)}{2}+\frac{(q)(q)}{3}\right]=k\left[-2q^2-q^2+\frac{q^2}{3}\right]=k\left[-3q^2+\frac{q^2}{3}\right]=-\frac{8kq^2}{3}$$

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