Question

A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium, if $q$ is equal to

• A. $- \frac{Q}{2}$
• B. $- \frac{Q}{4}$
• C. $+ \frac{Q}{4}$
• D. $+ \frac{Q}{2}$

Answer 1

Answer: (B)

$- \frac{Q}{4}$

Answer 2

Suppose in the following figure, equilibrium of charge B is considered. Hence for it's equilibrium

$|F_{A}| = |F_{C}|$

⇒ $\frac { 1 } { 4 \pi \varepsilon _ { 0 } } \frac { Q ^ { 2 } } { 4 x ^ { 2 } } =$ $\frac{1}{4\pi\varepsilon_{0}}\frac{qQ}{x^{2}}$ ⇒ $q = \frac{- Q}{4}$

Short Trick : For such type of problem the magnitude of middle charge can be determined if either of the extreme charge is in equilibrium by using the following formula.

q = – $Q_{B}\left( \frac{x_{1}}{x} \right)^{2}$

If charge B is in equilibrium then

$q = - Q_{A}\left( \frac{x_{2}}{x} \right)^{2}$

If the whole system is in equilibrium then use either of the above formula.