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A conducting coil having 500 turns has a cross-sectional area of 0.15 m². A magnetic field of 0.2 T, perpendicular to this area, changes to 1.0 T in 0.4 s. The induced emf produced in the coil will be ______ volt.

Asked in GUJCET 2014 · Flux change and induced EMF

• (1) 10.0
• (2) 15.0
• (3) 75.0
• (4) 150.0

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 10.0 V. Sanity check: one turn alone gives A (Δ B)/(Δ t) = 0.15 × (0.8)/(0.4) = 0.3 V, and 500 turns in series give 150 V.
• (2) No single slip gives 15.0 V; it is one-tenth of the correct value. Check: NA (Δ B)/(Δ t) = 500 × 0.15 × 2 = 150 V.
• (3) No single slip gives 75.0 V; it is half the correct value. Sanity check: Δ B = 1.0 - 0.2 = 0.8 T in 0.4 s is a rate of 2 T s⁻¹, so the emf is 500 × 0.15 × 2 = 150 V.

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