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ExamsGATEEngineering Mathematics

In cylindrical coordinate system, the potential produced by a uniform ring charge is given by φ = f(r,z), where f is a continuous function of r and z. Let E be the resulting electric field. Then the magnitude of ∇ × E is ________.

  1. (A) increases with r.
  2. (B) is 0.
  3. (C) is 3.
  4. (D) decreases with z.

Correct answer: (B) is 0.

Solution

The electric field produced by a static charge distribution, such as a uniform ring charge, is conservative, meaning that the curl of the electric field (∇ × E) is zero. This is a fundamental property of electrostatics, indicating that the electric field can be derived from a scalar potential function.

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