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

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

AIPMTAIPMT 1995Electrostatic Potential and Capacitance

Solution:

For equilibrium of charge Q, the force of repulsion due to similar charges Q should be balanced by the force of attraction due to charge q and
$ \frac{1}{ 4 \pi \varepsilon_0 } \times \frac{ Q q}{ ( r / 2)^2 } + \frac{1}{ 4 \pi \varepsilon_0 } \times \frac{ Q^2 }{ r^2 } = 0 $
or $ 4 \times \frac{ Q}{ r^2 } q = - \frac{ Q^2 }{ r^2 }$ or $ 4q = - Q$ or $ q = - \frac{ Q}{ 4}$.