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Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point of the configuration Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart

Q 1.32(b):  Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

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Two charges of same magnitude and sign are placed at a certain distance apart. The mid-point of the line joining these charges will have E =0.

When a test charged is displaced along the line towards the charges, it experiences a restoring force(which is the condition for stable equilibrium). But if the test charge is displaced along the normal of the line, the net electrostatic force pushes it away from the starting point. Hence, the equilibrium is unstable.

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