The GATE Grind

GATE 2016 EE – Question 23

Electromagnetic Fields · Biot-Savart law, Ampere law, Curl, Faraday law, Lorentz force · 1 mark · Multiple choice

In cylindrical coordinate system, the potential produced by a uniform ring charge is given by $\varphi = f(r, z)$, where $f$ is a continuous function of $r$ and $z$. Let $\vec{E}$ be the resulting electric field. Then the magnitude of $\nabla \times \vec{E}$

  1. increases with $r$.
  2. is 0.
  3. is 3.
  4. decreases with $z$.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) is 0.

Explanation

The electric field from a potential is $\vec{E} = -\nabla\varphi$. The curl of the gradient of any scalar function is zero, so $\nabla \times \vec{E} = 0$.