Question

Two free point charges +q and +4q are at the co-ordinates (0,0) and (a, 0). A third charge is placed on the line joining them so that the entire system is in equilibrium. The value and position of the third charge is

• A. $-\frac{4q}{9}at(\frac{a}{3},0)$
• B. $\frac{2q}{3}at(\frac{a}{3},0)$
• C. $-\frac{2q}{3}at(\frac{a}{2},0)$
• D. $\frac{4q}{9}at(\frac{2a}{3},0)$

Answer 1

The correct option is A $-\frac{4q}{9}at(\frac{a}{3},0)$

$x=\frac{d}{\sqrt{\frac{q_2}{q_1}}+1}=\frac{a}{\sqrt{\frac{4q}{q}}+1}=\frac{a}{3}(y=0)$
$\underset{F_{12}}{\to }+\underset{F_{13}}{\to }=0$
$\frac{1}{4\pi {ϵ}_0}\frac{qQ}{\left(\frac{a^2}{9}\right)}=-\frac{1}{4\pi {ϵ}_0}\frac{q\times 4q}{a^2}$
$Q=-\frac{4q}{9}$