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Question
Why must electrostatic field be normal to the surface at every point of a charged conductor?
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Solution
In case of conductors the charge is present only on the outer surface. Inside the conductor the field is zero. And at the surface it has to be normal. If it is not normal to the surface, then it would have some non-zero component along the surface. The free charges on the surface would then experience a force and start moving. In a static situation, electrostatic field should not have tangential component, which in turn implies that the surface of a charged conductor must be normal to the surface at every point. If a conductor has no surface charge, then the field is zero.
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