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(a) Let the equilibrium of thetest charge be stable. If a test charge is in equilibrium and displaced fromits position in any direction, then it experiences a restoring force towards anull point, where the electric field is zero. All the field lines near the nullpoint are directed inwards towards the null point. There is a net inward fluxof electric field through a closed surface around the null point. According toGauss’s law, the flux of electric field through a surface, which is notenclosing any charge, is zero. Hence, the equilibrium of the test charge can bestable.
(b) Two charges of samemagnitude and same sign are placed at a certain distance. The mid-point of thejoining line of the charges is the null point. When a test charged is displacedalong the line, it experiences a restoring force. If it is displaced normal tothe joining line, then the net force takes it away from the null point. Hence,the charge is unstable because stability of equilibrium requires restoringforce in all directions.