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# Electromagnetic Induction of Wires

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Imagine in a remote area of the countryside a 70-kV, 60-Hz power line. A shifty local resident has erected a large open loop just below the line with the intention of drawing power. Is this possible and, if so, how would it be transferred? Where would the energy stolen come from? Would anyone be able to detect the loss? Might it be possible to bug a telephone using the same approach? Explain.
Problem

1. The magnetic field of a large electromagnet is a uniform 0.140 T directed east to west. A 10.0-cm length of straight copper wire is held horizontally in the field perpendicular to it and then moved downward at 0.50 m/s. What voltage will appear across the wire? Which end is
positive?

2. A straight 30-cm length of copper is moved at a constant speed of 0.50 m/s perpendicularly across a uniform magnetic field of 1.5 T. Determine the emf appearing across its ends.

3. An emf of 0.45 V is induced in a straight conductor having a length of 20 cm moving at right angles to a magnetic field at a constant speed of 600 cm/s. Calculate the value of the field.

4. A straight 1.00-m-long copper rod is moved perpendicularly across a uniform 0.11-T magnetic field. If a constant voltage of 0.50 V appears across its end, how much time will it take to traverse the 0.50-m-long field region?

5. If a current of 2.0 A in a coil produces a flux linkage of 6.0 mEb, what is the self-inductance?

6. Consider a 2.0mH coil carrying a 2.0 A clockwise. If the current drops to zero and rises in the opposite direction (counterclockwise) to 1.0 A in 500us, what average emf will appear across the coil?

##### Solution Summary

The electromagnetic induction of wires are examined. The voltage that appeared across the wire are given.

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1. Imagine in a remote area of the countryside a 70-kV, 60-Hz power line. A shifty local resident has erected a large open loop just below the line with the intention of drawing power. Is this possible and, if so, how would it be transferred? Where would the energy stolen come from? Would anyone be able to detect the loss? Might it be possible to bug a telephone using the same approach? Explain.

Since the power line is carrying alternating current the direction of the current is not uniform and a changing magnetic flux is produced which passes through the loop erected by the resident. As a result emf will be induced in the loop from which power can be drawn. However the magnitude of this power drawn will be very small and not possible to detect.
The stolen energy comes from the power line. The power is ...

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