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Q.

A charge q is placed at the mid – point of the line joining two charges each of Q. If the whole system is in equilibrium, then the value of q is

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a

$+ \frac{Q}{2}$

b

$- \frac{Q}{4}$

c

$- \frac{Q}{2}$

answer is C.

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Detailed Solution

Suppose equilibrium of charge B is considered. Hence for its equilibrium $|F_{A}| = |F_{B}|$

$\frac{1}{4 {πε}_{0}} \frac{Q^{2}}{4 x^{2}} = \frac{1}{4 {πε}_{0}} \frac{qQ}{x^{2}} \Rightarrow q = \frac{- Q}{4}$

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