# Electromagnetic induction, induced EMF – problems and solutions

1. A coil replaced with another coil that has loops 2 times the initial loops and the rate of change of magnetic flux is constant. Determine the ratio of initial and final induced emf.

Known :

Initial loops (N) = 1

Final loops (N) = 2

The rate of change of initial magnetic flux (ΔØB / Δt) = the rate of change of final magnetic flux (ΔØB / Δt)

Wanted: The ratio of initial and final induced emf

Solution :

The equation of Faraday’s law of induction :

E = -N (ΔØB / Δt)

E = induced EMF, N = number of loops, ΔØB / Δt = the rate of change of magnetic flux

The ratio of initial and final induced emf :

E initial: E final

-N (ΔØB / Δt) : -N (ΔØB / Δt)

1: 2

2. In the initial state (1), the magnetic flux is changed by 5 Wb in 2 seconds on a coil with 20 loops. In the final state (2), the same flux changed in 8 seconds. Determine the ratio of the initially induced emf and the final induced emf.

Known :

The rate of change of initial magnetic flux (ΔØB / Δt) = 5/2

The rate of change of final magnetic flux (ΔØB / Δt) = 5/8

Number of loops (N) = 20

Wanted: The ratio of the initially induced emf and the final induced emf

Solution :

E initial: E final

-N (ΔØB / Δt) : -N (ΔØB / Δt)

20 (5/2) : 20 (5/8)

5/2: 5/8

1/1: 1/4

4: 1

3. The magnetic flux of the initial coil has 200 loops changes by 0.06 Wb in 0.4 seconds. The magnetic flux of the final coil has 0.08 Wb in 0.2 seconds. If a number of loops of the final coils are substituted with the half number of the first coil’s loops, determine the ratio of the induced emf of the initial loops and the final loops.

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Known :

The rate of change of initial magnetic flux (ΔØB / Δt) = 0.06 / 0.4

Number of initial loops (N) = 200

The rate of change of final magnetic flux (ΔØB / Δt) = 0.08 / 0.2

Number of final loops (N) = 100

Wanted : The ratio of the initial induced emf and the final induced emf

Solution :

E initial : E final

-N (ΔØB / Δt) : -N (ΔØB / Δt)

200 (0.06/0.4) : 100 (0.08/0.2)

2 (0.15) : 1 (0.4)

0.3 : 0.4

3 : 4