Question

Three charged particles having charges q, -2q & q are placed in a line at points (-a, 0), (0, 0) & (a, 0) respectively. The expression for electric potential at P(r, 0) for r > > a is

• A. $\frac{1}{4\pi {ϵ}_0}\frac{q{a}^2}{r^4}$
• B. $\frac{1}{4\pi {ϵ}_0}\frac{8q{a}^2}{r}$
• C. $\frac{1}{4\pi {ϵ}_0}\frac{2q{a}^2}{r^3}$
• D. $\frac{1}{4\pi {ϵ}_0}\frac{4q{a}^2}{r^2}$

Answer 1

Answer: (C)

Electric potential is given by, $V=\frac{kq}{r}$, where $k=\frac{1}{4\pi {ϵ}_0}$

Total electric potential at point P, $V=\frac{kq}{r-a}+\frac{k(-2q)}{r}+\frac{kq}{r+a}$

$V=kq(\frac{r-a+r+a}{r^2-a^2}-\frac{2}{r})$

$V=kq(\frac{2r}{r^2-a^2}-\frac{2}{r})$

$V=kq\left(\frac{2r^2-2r^2+2a^2}{r(r^2-a^2)}\right)$

$V=kq\left(\frac{2a^2}{r(r^2-a^2)}\right)$

Since, $a<<r⟹a^2<<<r^2$,

$V=\frac{2kq{a}^2}{r^3}$