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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Solution

For the configuration of the two charges of the same magnitude and sign, the null point is the mid of the line joining the two charges.If the test charge is displaced slightly from the null point along the line, it all return back due to the restoring force that comes into the day. But if the charge is displaced slightly from the null-point along normal to the line it will not return. This is because the resultant force due to the configuration of two charges will take it away from the null point. For the test charge to be in stable equilibrium restoring force must come into play, when it is displaced in any direction. Hence the test charge cannot be in stable equilibrium.

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