Practice question
Question
A solenoid of 400 turns and length 0.5 m induces an emf of 0.8 V in a nearby coil when its current
changes from 2 A to 4 A in 0.2 s. What is the mutual inductance?
Explanation
**Solenoid carries steady current** second coil experiences emf only when current in solenoid changes because dΦ/dt ≠0 only when I changes, steady current gives constant flux, no induction, illustrating Faraday's law requires changing flux, not static field. ε = M (Δ I/Δ t) . Δ I = 4 - 2 = 2 A , Δ t = 0.2 s . M = (ε/(Δ I/Δ t)) = (0.8/(2/0.2)) = (0.8/10) = 0.08 H . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L = μ₀ N²A/l, M = e/(dI/dt) and
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