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# Investigate the factors affecting the induced e.m.f. in a coil due to the changing magnetic field in a neighbouring coil.

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Introduction

Physics Practical Report

The Law of Electromagnetic Induction

Objective:        To investigate the factors affecting the induced e.m.f. in a coil due to the changing magnetic field in a neighbouring coil.

Apparatus:        Two square solenoids with different sizes, a CRO, a signal generator, an ammeter (1A a.c.), two PVC covered copper wires with different lengths, a magnetic field board, an axial search coil, connecting leads, a connecting plug.

## THEORIES

Faraday’s law states that the induced e.m.f. is directly proportional to the rate of change of flux-linkage or rate of flux cutting, i.e.

where  is the induced e.m.f. in a coil of N turns through which a magnetic flux  is passing.

The proportional constant is found to be 1. Therefore, we have

The magnetic flux  is defined as the product of the flux density normal to the surface and the area of the surface, i.e.

Therefore, the induced e.m.f. is found to be

Hence, the factors affecting the induced e.m.f. in a coil due to the changing magnetic field in a neighbouring coil are rate of change of magnetic field (frequency of A.C. supply,f), magnetic field strength (current through the solenoid, B), number of turns of coil N, the area of surface of solenoid A

Middle

At the beginning of the experiment, the frequency of signal generator is set at 500Hz. The current is set at 860mA. The smaller square solenoid is used. l is the peak-to-peak reading in C.R.O.

The frequency is changed to investigate its effect on induced e.m.f. The current is kept constant every time whenever the frequency is changed.

Investigation 1:        Rate of Change

Results:

 f / Hz 500 600 700 800 900 100 l / cm 3 3.4 4 4.4 4.6 4.9

The graph of l against f is drawn on a separate graph paper (GRAPH 1).

Measurements:

From the graph, it can be said that the relation between l and f is linear. Although several points are quite far from the lines, three of the points can be connected firmly in a straight line.

Then the frequency is reset to 500Hz. The smaller square solenoid is used.

The current supply is changed this time to investigate its effect on induced e.m.f.

Investigation 2:        Field

Results:

 I / mA 100 200 400 600 800 1000 l / cm 0.4 0.8 1.5 2.2 2.8 3.6

The graph of l against I is drawn on a separate graph paper.

Measurements:

From the graph, it is easily observed that the relation between l and I is linear as the points nearly lie in a straight line (GRAPH 2).

Then the frequency is kept at 500Hz. The smaller square solenoid is used. The current is also kept constant at 860mA.

Conclusion

Sources of errors

1.        The frequency of A.C. generated by the signal generator might not be correct. When the experiment was carried out, it was found that 10 x 100Hz was very different from 1 x 1kHz as seen on the C.R.O. screen where the latter one had a high level of inaccuracy. It had been assumed that the frequency indicated on the signal generator was correct. However, this might not be a significant source of error in finding out just the relationship between induced e.m.f. and frequency since the induced e.m.f. could still increase with increasing frequency.

2.        The ends of the wires around the solenoid could induce e.m.f. However, this seems not to be a significant source of error because the effect is quite small unless the ends of the wires are put around the solenoid.

3.        The axial search coil should be put in the centre of the 10-turn coil. Otherwise, the result obtain would not be the maximum value which may affect the angle through which the axis of the search coil.

Possible Improvements

1. Measure the frequency generated by the signal generator each time when the effect of varying frequency on induced e.m.f. is observed to ensure the signal generator gives out desired frequency.
2. Place the search coil as near in the centre of the 10-turn coil as possible to reduce the error.

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