Verified Solution • 2025–26 Session moderate

QPages 306-313: Q58: HC Verma: Concepts of Physics - Volume 2 Electromagnetic Induction Pages 306-313: Q58 Solution: A rectangular metallic loop of length l and width b is placed…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat the magnetic field of the long wire as uniform across the loop’s width and apply ε = Bℓv with a single B value, which discards the 1/r variation and the resulting logarithmic dependence. Remember to integrate B = μ₀i/(2πr) over the moving side (or differentiate the flux with both limits moving) to obtain the correct emf.

A rectangular metallic loop of length l and width b is placed coplanarly with a long wire carrying a current i figure). The loop is moved perpendicular to the wire with a speed v in the plane containing the wire and the loop. Calculate the emf induced in the loop when the rear end of the loop is at a distance a from the wire. Solve by using Faraday's law for the flux through the loop and also by replacing different segments with equivalent batteries.

Step-by-Step Verified Solution

**Answer:** _ = (__iv/2�) ln[(a+b)/a]. **Step-by-Step Explanation:** As the loop moves away from the wire, the flux changes. _ = -d_/dt. Also derivable by replacing segments with equivalent batteries [citation:3].

All Questions in this Chapter

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