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Consider an arbitrary electrostatic field configuration A small test charge is placed at a null point ( i.e., where vec(E) = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable. |
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Answer» Solution :Let us assume the free charge to remain in stable equilibrium. Under this CONDITION the test chargewould return to its original positive of neutral point when deflected SLIGHTLY in any direction. This implies that all the field linear near the neutral point are directed towards it. This proves the existence of inward bound electric flux ASSOCIATED with the imaginary Gaussian surface SURROUNDING the point. But according to Gauss' theorem the flux associated with a closed surface in the absence of any enclosed charge is zero. Hence our assumption was not correct, i.e., the free charge should remain in UNSTABLE equilibrium. |
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