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GATE 2026 IN – Question 38

Electricity and Magnetism · Magnetic fields and induction · 2 marks · Multiple choice

A straight thin wire carrying a current $I=1\ \mathrm A$ in the direction $\hat n=(\hat i+2\hat j+\hat k)/\sqrt6$ is placed inside a magnetic field $\vec B=(2\hat i+2\hat k)\ \mathrm T$. The force per unit length on the wire is ________ N/m.

  1. $2\sqrt6\hat i-2\sqrt6\hat k$
  2. $\sqrt{\frac32}\hat i-\sqrt{\frac34}\hat j+\sqrt{\frac34}\hat k$
  3. $\frac4{\sqrt6}\hat i-\frac4{\sqrt6}\hat k$
  4. $\sqrt{\frac32}\hat i+\sqrt{\frac34}\hat j+\sqrt{\frac34}\hat k$

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Show answer and explanation

Correct answer: (C) $\frac4{\sqrt6}\hat i-\frac4{\sqrt6}\hat k$

Explanation

The magnetic force per unit length is $\vec F/\ell=I(\hat n\times\vec B)$. Evaluating the cross product gives $\hat n\times\vec B=[(2\times2-1\times0)\hat i+(1\times2-1\times2)\hat j+(1\times0-2\times2)\hat k]/\sqrt6$.

With $I=1\ \mathrm A$, $\vec F/\ell=(4\hat i-4\hat k)/\sqrt6\ \mathrm{N/m}$. The correct option is **C**.