Consider an arbitrary electrostatic field configuration. A small test total is placed at a null point (i.e, where ` oversetto E=0 ` ) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.
(b) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

Explanation

Let us presume that the equilibrium of the test charges at the null-point is stable .Then the test charges displaced slightly in any direction must experience a restoring force towards the null-point. It means that all field lines near the null-point should be directed inwards towards the null-point However , by Gauss.s law the electric flux through a surface not enclosing any charges, must be zero -Hence or presumption is wrong or it means that the equilibrium of the test charge at the null-point is necessary unstable.
(b) We know that if two charges of same magnitude and sign are placed a certain distance apart, the mid-point of the line joining two charges is a ull-point.Displace the test charges placed at neutral point slightly in a normal direction. We find that the a net force acts now on the test charges and takes it away from the neutral point i.e., test charges does not return to the null- point . It shows that the equilibrium is a unstable equilibrium.