1) An experiment was conducted to verify Faraday's law of induction using a hand-crank generator with different coil configurations. 2) The results showed that increasing the number of coil loops or the rotation speed increased the induced electromotive force (EMF), as predicted. 3) However, inconsistencies in measuring the magnetic field introduced errors, so the data was not considered accurate enough to conclusively prove the theory. Improving the magnetic field measurements would strengthen future experiments.

1. By
Vijayan Thanasekaran
Matthew.t.mackarevich
William Lam
Hannah Kim
Induced EMF
Verifying Faraday’s Law of Induction using electric generator

2. Theory
● Faraday’s Law
● Magnetic Flux
● Electromagnetic Induction
● Questions proposed:
○ Can we create more potential energy in a copper wire loop that is penetrated by a
fixed magnetic field by increasing the number of loops in that wire?
○ Can we also create more potential voltage in the copper wire loop by increasing
the rate of rotation in a magnetic field?

3. Hypothesis
● The prediction is that with a fixed magnetic field, if the induced voltage in a copper
wire is increased as well as the surface area of the wire loop (in terms of
increasing the number of loops), the rate of change of the magnetic flux through
that wire increases.

4. inducing sinusoidal emf
● We can generate Faraday induction volt by oscillating area
○ A(t) = A sin (ωt)
○ So, V(t) = -NBωA cos(ωt) • Since the coil is rotating against the
direction of magnetic flux, The maximum
EMF is generated when the coil to parallel
to magnetic flux. And zero when
perpendicular.
• The rotating coil is going up and down, so
the direction of EMF is changed every up
and down.
• These two factor cause the generated emf
sinusoidal, which is alternating current.

5. Procedure: Creating Hand Crank Generator
1. Create coil
2. Create circuit (positive and negative end of electric power outlet)
3. Combine copper axle with a small wheel
4. Small wheel is connected to a big wheel
5. Magnet placed underneath
6. Rotate the wheel

6. The coil
• Thin Insulated coper wire is winded around square shaped wood.
• 3.8cm x 3.8 cm = 0.001444 meter

7. Setup
Small copper wire
Attached and pressed
against the axle with
the help of rubber band

8. Functioning setup

9. Procedure: Experiment
1. Establish: area of coil, number of coils, loops of coils
2. With multimeter measure the magnetic field of the magnet
3. Attach oscilloscope to the wire
4. Establish what speeds the coil will rotate at
5. Record oscillations and highest EMF produced

10. Three coils have different turn count

12. 50 turns
23 cycles
(0.008v)
Same count with different speed
for 5.3 seconds of duration
50 turns
34 cycles
(0.012v)
50 turns
64 cycles
(0.017v)

13. Different count with same speed
for 5.3 seconds of duration
50 turns
34 cycles
(0.012v)
100 turns
34 cycles
(0.023v)
200 turns
34 cycle
(0.045v)

14. Data:
Calculated Data:
● Area (square): l*l = 0.00144
● Magnetic Field in Tesla: 3.5 *(3.2*10^-3) = 0.0112
● Revolutions/s: number of rotations/time = 19 rot/ 5.3 s = 3.58 rot/s
● Angular Velocity: 2*π*f = 2π*(3.58 rot/s) = 22.52
● Average EMF generated: N*B*ω*A = 50*0.0112*22.52*0.00144 = 0.0182

15. data table

16. Actual produced Vs calculated emf
0.0000
0.0100
0.0200
0.0300
0.0400
0.0500
0.0600
0.0700
0.0800
0.0900
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Actual Vs Calculated
Voltage produced
(Observed in the experment)
(v)
Average EMF Calculated
(NBωA)
(v`)
Produced emf is bigger than the calculated emf.
It may because of the faulty magnetic probe.
It looks that the measured flux is lower than the actual

17. Actual produced Vs calculated emf
0.0000
0.0100
0.0200
0.0300
0.0400
0.0500
0.0600
0.0700
0.0800
0.0900
1 3 5 7 9 11 13 15 17 19 21 23 25 27
Voltage produced
(Observed in the experment)
(v)
0.00000000
0.00500000
0.01000000
0.01500000
0.02000000
0.02500000
1 3 5 7 9 11 13 15 17 19 21 23 25 27
Average EMF Calculated
(NBωA)
(v`)
Both looks similar if we scale it to same size.
It means that our system and experiments were gone correctly

18. Square if deviation
0.00000000
0.00100000
0.00200000
0.00300000
0.00400000
0.00500000
0.00600000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Actual EMF Produced
Square of deviation
ε2 = (v-<v>)2
• The produced EMF is deviated moderately with the experiments done by the coil turn count of 50.
• Not deviated much for the coil turn count 100.
• It is deviated much for the coli turn count 200 and faster rotation of coil.
The curve shows that the emf is increased linearly based on number of turns and angular velocity.

19. Errors
N error
(δN)
G error
(δG)
2 3.2x10-4
0.000
0.020
0.040
0.060
0.080
0.100
0.120
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Voltage produced
Error Propagation
(v)
The error is enlarged as more EMF is produced. See the smaller turn count of coil
with slow speed shows minimal error. The error is enlarged in the bigger turn count with faster speed

20. Computing actual Magnetic flux
Actually we are not getting the produced EMF matched with the actual calculation. And we know that the iss
It is expected to get constant value of Magnetic flux throughout the experiments.
So the magnetic field G = v / (NωA)

21. Computing actual Magnetic flux
The average Magnetic flux <B> = 0.004017 tesla.
Since it is constant in all experiment, the plotted graph is expected to be a straight line.
And yes The trend line shows that straight line around 0.004 tesla.
0.00000000
0.00500000
0.01000000
0.01500000
0.02000000
0.02500000
0.03000000
0 5 10 15 20 25 30
Computed Magnetic field
B= v/(NωA)

24. Analysis
● Magnetic field in volts -> tesla
● Rotation/second
● Angular velocity
● EMF produced vs. calculated average EMF generated
● Most likely data would be considered inaccurate and not significant enough to
prove the theory proposed

25. Conclusion
● Measured induced EMF increased as we increased the number of loops,
increase rate of rotation in the copper coil loop
● Factor that could have influenced our results was the measurement of our
constant magnetic field.
● Another factor was flux change with respect to distance from the magnet.
● Improvements: consistent flux change and more reliable measuring devices
● What’s next?