A square loop with 100 turns, area 2.5×10⁻³ m² and total resistance 100 Ω is slowly and uniformly withdrawn from a B = 0.40 T field over 1.0 s. The work performed by the external agent is n×10⁻⁴ J. Find n.
Physics · Mixed Chapter
JEE Mains

Question

A square loop with 100 turns, area 2.5×10⁻³ m² and total resistance 100 Ω is slowly and uniformly withdrawn from a B = 0.40 T field over 1.0 s. The work performed by the external agent is n×10⁻⁴ J. Find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Initial magnetic flux through the coil: Number of turns N = 100, area per turn A = 2.5×10⁻³ m² and uniform field B = 0.40 T. Initial flux linkage = NBA. Step 2 — Induced emf while withdrawing: The entire loop is pulled out in Δt = 1.0 s. Average emf magnitude = NBA/Δt = 100×0.40×2.5×10⁻³/1.0 = 0.10 V. Step 3 — Induced current and mechanical work: Coil resistance R = 100 Ω, so I = 0.10/100 = 0.001 A. At slow, uniform motion the external work equals Joule heat: W = I²RΔt = (0.001)²×100×1…