Now imagine that the coil is subjected to a series of experiments, that we will label 1, 2, etc., for clarity. At the beginning of both experiments 1 and 2, the magnetic field is initially 3.0 T. In experiment 1, the magnetic field is changed in 2.0 ms from 3.0 T to 6.0 T. In experiment 2, the magnetic field is changed in 2.0 ms from 3.0 T to 20.0 T. What is the ratio of the average emf observed in each case, EMF1 / EMF2?

EMF1/EMF2 = 3/17 = 0.176

Explanation:

Experiment 1:

B₁ = 3.0 T

B₂ = 6.0 T

dt = 2 ms

dB = B₂ - B₁ = 6 T-3 T

dB = 3 T

Now

∅ = B*A cosθ (A is area of the coil)

d∅ = dB*A cosθ

d∅ = 3*A cosθ

Average emf

ε₁ = d∅/dt

ε₁=3*A cosθ / 2*10^-3

ε₁=1500*A*cosθ

Experiment 2:

B₁ = 3.0 T

B₂ = 20.0 T

dt = 2 ms

dB = B₂ - B₁ = 20 T-3 T

dB = 17 T

Now

∅ = B*A cosθ (A is area of the coil)

d∅ = dB*A cosθ

d∅ = 17*A cosθ

Average emf

ε₂ = d∅/dt

ε₂=17*A cosθ / 2*10^-3

ε₂=8500*A*cosθ

Ratio of average emf:

EMF1/EMF2 = ε₁/ε₂ = (1500*A*cosθ) / (8500*A*cosθ)

EMF1/EMF2 = 1500/8500

EMF1/EMF2 = 3/17 = 0.176