Question:
(a) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where 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.
Answer:
a) Let us consider that initially the rest charge is in the stable equilibrium .
When the rest charge is taken away from the null point (i.e) E=0E=0 , in any direction , it must experience a restoring force towards the null point.
b) The middle point of the line joining two like charges is a null point.
If we take a test charge slightly away from the point along the line, the restoring force. will try to bring it back to the centre.
If we take the rest change normal to the line, the net force on the test charge takes it further away from the null point.
Therefore the equilibrium is not stable.
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