two coils are wound around the same cylindrical form, like the coils in example 30.1. when the current in the first coil is decreasing at a rate of -0.242 a>s, the induced emf in the second coil has magnitude 1.65 * 10-3 v. (a) what is the mutual inductance of the pair of coils? (b) if the second coil has 25 turns, what is the flux through each turn when the current in the first coil equals 1.20 a? (c) if the current in the second coil increases at a rate of 0.360 a>s, what is the magnitude of the induced emf in the first coil?

When the bar magnet is pushed out, an electromotive force is induced in the coil. An EMF of opposite sign is produced by moving in the opposite direction, and the EMF is also flipped by reversing the poles. You can get the same result by moving the coil instead of the magnet - relative motion is important.

For mutual inductance:

M = ∈/(Δi/Δ)

Where, M = mutual inductance

∈ = 1.65 × 10⁻³ V

Δi/Δt = -0.242 A/s

M = 1.65 × 10⁻³/ -0.242

M = 6.818 × 10⁻³ Hz or 6.818 mHz

For the calculation of the flux through each turn:

∅ = MI/N

Where, ∅ = Total flux

M = Mutual inductance

I = Current through one coil

N = Number of turns

∅ = (6.818 × 10⁻³ × 1.20)/25

∅ = 3.27 × 10⁻⁴ Wb

For induced EMF:

∈ = M × (Δi/Δt)

∈ = induced EMF

M = 6.818 × 10⁻³ Hz

Δi/Δt = 0.360 A/s

∈ = 6.818 × 10⁻³ × 0.360

∈ = 2.45 × 10⁻³ V

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