Magnetic Flux and Potential Difference
Date: Spring 2012
If a conducting loop is placed in a changing magnetic field, it will gain an induced emf that is equal to the opposite of the rate of change of the magnetic flux through its internal area with respect to time. Can this induced voltage be measured as a voltage drop along some portion of the wire? After all, we normally think of voltage as a difference between two points in space. Can we used that understanding when dealing with an induced emf in a loop?
Yes. There is a measurable EMF in the loop. If the loop is fine wire wound tightly, the magnet very strong and one of them is moving… the EMF can be considerable. In a practical sense, we use this principle as a generator or alternator.
The spinning may be from any source of energy. There is sufficient energy in water flow, wave action or wind source to power many homes using the technlogy.
Peter E. Hughes, Ph. D.
Yes, Hari, it can be measured in the same way, although in this case it would be acting more like a voltage source than a drop. (Not that this makes a difference when it comes to measuring it.) No matter what movement produces it, the flow of electrons will have a direction at any given moment in time, so a meter connected to the wire ends of the loop would be able to detect the induced voltage. You're also correct that there would be a voltage drop across the conductor due to whatever electrical resistance it has. We ordinarily would think of this voltage drop as spread across the length of the conductor, but if you were to measure some shorter portion of it you would measure the voltage dropped over that portion.
In fact, (as you probably know) this is how the electricity in our houses is generated--a coil is effected by a changing magnetic field.
As I think you gather, there are great many additional things that could be discussed related to your coil in the moving magnetic field that could be researched if you are so inclined. They form the basis for understanding transformers, generators, electric motors and more!
I hope this helps.
Because the loop has essentially no resistance, putting a voltage sensor to two places on the wire will not work well. Not enough current will flow through the sensor to register. The sensor will be “shorted out” by the piece of wire. A better way involves a resistor. Put a small resistor in the loop. Make it part of the loop. Because the resistor is in series with the rest of the loop, almost all of the emf will be on the resistor. Now, put the voltage sensor across the resistor. The resistor will ensure that a tiny bit of current flows through the sensor, enough to register a voltage. The resistance of the resistor will be much smaller than that of the sensor, so the sensor will not affect what happens in the loop very much at all.
If you want to see the emf distributed around the loop, make a loop of ten equal resistors in series. Measure each voltage separately, and see what the sum is.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012