A charge ' $q$ ' is placed at the middle point of the line joining two equal charges ' $Q$ ' each. T

Question

A charge ' $q$ ' is placed at the middle point of the line joining two equal charges ' $Q$ ' each. The system of three charges will be in equilibrium if ' $q$ ' is equal to\

Professor PC Thomas Classes · Answer

The middle charge $q$ will be in equilibrium, what ever be the end charges, provided they are equal and like charges. For the equilibrium of the end charges, force on Q by Q must be equal and opposite to the force on Q by q\ ie $\frac{\mathrm{Q} 	imes \mathrm{Q}}{(2 \mathrm{r})^{2}}=-\frac{\mathrm{qQ}}{\mathrm{r}^{2}} \quad \mathrm{q}=\frac{-\mathrm{Q}}{4}$\