GATE EE 2016 Set 1 — Question 23
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Electromagnetic Fields → Electrostatics → Field & Potential of Charges
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Question
In cylindrical coordinate system, the potential produced by a uniform ring charge is given by , where is a continuous function of and . Let be the resulting electric field. Then the magnitude of
Correct answer
(B) is 0.
Solution
In electrostatics, the electric field is conservative and can be expressed as the negative gradient of a scalar potential : . A fundamental vector calculus identity states that the curl of any gradient field is zero: . Therefore, .
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