Tuesday 7-23-96
Note that the term electromotive force (emf) is simply another way of saying voltage, or potential difference.
Part of chapter 18 dealt with how a magnetic field is created by a current. Electric charges standing still do not set up magnetic fields; the charges have to be moving to create a magnetic field. Chapter 19 extends the inter-connection between electricity and magnetism, and shows how currents can be created by a magnetic field. The magnetic field must be changing to set up a current.
More accurately, the magnetic flux must be changing to induce an emf that can drive a current through a wire. The magnetic flux is a measure of the number of magnetic field lines. Consider a loop of area A in a magnetic field B. The flux, represented by the Greek letter capital phi, is given by
where theta is the angle between B and the vector representing the area of the loop (A), which is perpendicular to the plane of the loop.
Faraday's law of induction: An emf is induced in a loop by changing the magnetic flux through the loop.
One way to do this is to take a coil of wire (i.e., a solenoid) and bring a magnet near to it. If the magnet is held in one position near, or even inside the coil, no voltage will be induced because the magnetic field (and therefore the flux) will be constant. By moving the magnet back and forth near the coil, however, the magnetic field will change, changing the flux through the loop. This induces an emf (i.e., voltage) and therefore a current, in the loop.
Another way to induce an emf is to take the same coil of wire and place it near a second coil of wire. If a current is passed through the second coil, a magnetic field will be set up. Changing the current in the coil changes the magnetic field, which will change the flux through the first coil, inducing an emf and current in the first coil.
Lenz's law: The induced emf generates a current that sets up a magnetic field which acts to oppose the change in flux.
Another way of stating Lenz's law is to say that coils and loops like to maintain the status quo (i.e., they don't like change). If a coil has zero magnetic flux, when a magnet is brought close the coil will set up its own magnetic field which acts to cancel the field from the magnet. On the other hand, a coil with a particular flux from an external field will set up its own field to maintain the flux if the external field (and therefore flux) is reduced.
Faraday's law, the fact that an induced emf (i.e., voltage) is induced by a changing magnetic flux, can be expressed as an equation. The induced emf in a coil of N loops produced by a change in flux in a certain time interval is given by:
Recalling that the flux through a loop of area A is given by F = BA cos(theta), this equation can be written:
There are therefore three ways that an emf (i.e., voltage) can be induced in a loop:
Demonstrations relevant to this section: