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GATE 2025 IN – Question 30

Electricity and Magnetism · Magnetic fields and induction · 1 mark · Multiple choice

A 60 V DC source with internal resistance $R_{int}=0.5\ \Omega$ is connected through a switch to infinitely long rails separated by $l=1$ m, as shown. They lie in a uniform magnetic field $B=0.5$ T directed into the page. A conducting bar moves freely on the rails. At switch closure, the induced force is ______. Assume no friction and zero rail/bar resistance.

Diagram for GATE 2025 IN question 30
  1. 60 N in the $+\hat x$ direction
  2. 60 N opposite to $\hat x$
  3. 120 N in the $+\hat x$ direction
  4. 120 N opposite to $\hat x$

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Show answer and explanation

Correct answer: (A) 60 N in the $+\hat x$ direction

Explanation

At switch closure the stationary bar has no motional back emf.

Current is 60/0.5=120 A, so force magnitude is BIl=0.5×120×1=60 N.

With the shown current and field into the page, the right-hand rule gives **+x direction, A**.