Magnetic Induction

We have seen in our coverage of capacitance how a charged object brought near a conductor induces an opposite charge to form on the conductor's surface. The result is an attraction between the two, whether the charged object is at rest or moving.

For magnetism, there are similarities and differences. When a bar magnet is brought near a closed loop of wire (a conducting ring), an electrical current is induced to flow around the loop. But unlike the induction of surface charge, the current is induced only while the magnet is moving. If the magnet is held motionless, close to or far from the loop, no current flows.

Also unlike surface charge induction, the loop produces its own magnetic poles which repel the bar magnet if it is approaching the loop, or pull back on the bar magnet if it is moving away.

If the bar magnet is moved by hand, a very small resistive force is felt no matter which way it is moved: in fact, this is required since energy is conserved-- mechanical work must be done against resisting force (drag) if current is to be induced in the loop.
In any situation where the number of magnetic field lines passing through the open area of a loop (magnetic flux) is changing, a current will be induced in the loop. Besides this case, other ways to change magnetic flux through the loop include translating the loop rather than the magnet, rotating the loop, and changing the size or shape of the loop. Defining magnetic flux as
F_B = B_^A
The general equation, known as Faraday's Law of Induction, states that the rate of flux change is proportional to the voltage (electromotive force) induced in a coil of N turns:
e.m.f. = - N(DF_B/Dt)
The negative sign is to remind us of Lenz's Law: the e.m.f. produces a current, which produces an internal magnetic field around the coil, and this internal field always acts to oppose the change in the external magnetic field. This is related to the coil repelling an approaching magnet and pulling back on a receding magnet. It also relates to the action of an A.C. generator (a.k.a. alternator). An armature, rotating between the poles of a horseshoe magnet, experiences a changing magnetic flux and therefore has a current induced in it. The current behaves sinusoidally as the coil rotates with constant angular velocity (Alternating Current, or A.C.), because the coil alternately gets increasing and decreasing magnetic flux, causing the polarity of the e.m.f. to switch. Without getting into more detail, suffice it to say that the armature of the generator is turned mechanically, and input work is required in order to make the electricity flow in the armature coil. The source of the mechanical "resistance" felt when turning the armature is actually the attractive and repulsive forces between the armature's internal magnetic poles, and the horseshoe magnet's external magnetic poles.

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