Question

Show that the work necessary to assemble a static charge distribution (against the coulomb repulsion of like charges)

Answer 1

Assume charge is static (q)

Force repulsion mean

$q_1=q,q_2=q$

Between charge distance =r

$F=\frac{kq_1q_2}{r^2}$

Put value

$F=\frac{kq^2}{r^2}$ Repulsion force

Work (W)

$W=-\frac{kq_1q_2}{r}$

$W=-\frac{kq^2}{r}$

∆U=W=$\frac{kq^2}{r}$