**3 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 (ΔØ_{B }/ Δt) = the rate of change of final magnetic flux (ΔØ_{B }/ Δt)

__Wanted:__ The ratio of initial and final induced emf

__Solution :__

__The equation of Faraday’s law of induction :__

E = -N (ΔØ_{B }/ Δt)

*E = induced EMF, N = number of loops, ΔØ*_{B }*/ Δt = the rate of change of magnetic flux*

__The ratio of initial and final induced emf :__

E initial: E final

-N (ΔØ_{B }/ Δt) : -N (ΔØ_{B }/ 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 (ΔØ_{B }/ Δt) = 5/2

The rate of change of final magnetic flux (ΔØ_{B }/ 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 (ΔØ_{B }/ Δt) : -N (ΔØ_{B }/ 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.

__Known :__

The rate of change of initial magnetic flux (ΔØ_{B }/ Δt) = 0.06 / 0.4

Number of initial loops (N) = 200

The rate of change of final magnetic flux (ΔØ_{B }/ 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 (ΔØ_{B }/ Δt) : -N (ΔØ_{B }/ Δt)

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

2 (0.15) : 1 (0.4)

0.3 : 0.4

3 : 4