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Consider an arbitrary electrostatic field configuration. A small test total is placed at a null point (i.e,whereoversetto E=0)of the configuration. Show that the equilibriumof the testchargeis necessarilyunstable. (b)Verify this result for the simpleconfiguration of two charges of the same magnitudeand sign placed a certaindistance apart. |
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Answer» Solution :Let uspresume that the equilibriumof the test chargesat the NULL-pointis stable .Then the testchargesdisplacedslightly in anydirectionmustexperience a restoringforcetowards the null-point.It meansthat all field lines NEAR the null-point should be directedinwardstowardsthe null-pointHowever , by Gauss.s lawthe electricfluxthrough a surfacenot enclosing any CHARGES, mustbe zero -Henceor presumption is wrongor itmeans that the equilibriumof thetest charge at the null-pointis necessaryunstable. (b)We know that if two charges of same magnitude and sign are placed a certaindistance apart, the mid-pointof the line joining two charges is a ull-point.Displace the testcharges placed at NEUTRAL point slightlyin a normal direction. Wefind that the a net forceacts now on the test charges and takes it away from the neutral point i.e., testchargesdoes not returnto the null- point . It showsthat the equilibriumis a UNSTABLE equilibrium. |
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