7-20-00
Sections 21.3 - 21.6
Electromagnetic induction is an incredibly useful phenomenon with a wide variety of applications. Induction is used in power generation and power transmission, and it's worth taking a look at how that's done. There are other effects with some interesting applications to consider, too, such as motional emf and eddy currents.
Let's say you have a metal rod, and decide to connect that to your galvanometer. If the rod is stationary in a magnetic field, nothing happens. If you move the rod through the field, however, an emf is induced between the ends of the rod causing current to flow. This is because when you move the metal rod through the field, you are moving all the electrons in the rod. These moving charges are deflected by the field toward one end of the rod, creating a potential difference. This is known as motional emf. Motional emf can even be measured on airplanes. As the plane flies through the Earth's magnetic field, an emf is induced between the wingtips.
Motional emf is largest when the direction of motion of the piece of metal is perpendicular to the rod and perpendicular to the magnetic field. When this is true, the motional emf is proportional to the speed of the rod, the length (L) of the rod, and the magnetic field:
If the metal rod is part of a complete circuit, the induced emf will cause a current to flow. Because it's in a magnetic field, the rod experiences a force because of the interaction between the field and the current. This force always acts to oppose the motion of the rod.
When we looked at DC motors, we saw how the force exerted on a current flowing around a coil in a magnetic field can produce rotation, transforming electrical energy to mechanical energy. Motional emf is a good example of how mechanical energy, energy associated with motion, can be transformed to electrical energy.
An eddy current is a swirling current set up in a conductor in response to a changing magnetic field. By Lenzıs law, the current swirls in such a way as to create a magnetic field opposing the change; to do this in a conductor, electrons swirl in a plane perpendicular to the magnetic field.
Because of the tendency of eddy currents to oppose, eddy currents cause energy to be lost. More accurately, eddy currents transform more useful forms of energy, such as kinetic energy, into heat, which is generally much less useful. In many applications the loss of useful energy is not particularly desirable, but there are some practical applications. One is in the brakes of some trains. During braking, the metal wheels are exposed to a magnetic field from an electromagnet, generating eddy currents in the wheels. The magnetic interaction between the applied field and the eddy currents acts to slow the wheels down. The faster the wheels are spinning, the stronger the effect, meaning that as the train slows the braking force is reduced, producing a smooth stopping motion.
A electric motor is a device for transforming electrical energy into mechanical energy; an electric generator does the reverse, using mechanical energy to generate electricity. At the heart of both motors and generators is a wire coil in a magnetic field. In fact, the same device can be used as a motor or a generator.
When the device is used as a motor, a current is passed through the coil. The interaction of the magnetic field with the current causes the coil to spin. To use the device as a generator, the coil can be spun, inducing a current in the coil.
An AC (alternating current) generator utilizes Faraday's law of induction, spinning a coil at a constant rate in a magnetic field to induce an oscillating emf. The coil area and the magnetic field are kept constant, so, by Faraday's law, the induced emf is given by:
If the loop spins at a constant rate, 
. Using calculus, and taking the derivative of the cosine to get a sine (as well as bringing out a factor of 
), it's easy to show that the emf can be expressed as:
The combination 
represents the maximum value of the generated voltage (i.e., emf) and can be shortened to 
. This reduces the expression for the emf to:
In other words, a coil of wire spun in a magnetic field at a constant rate will produce AC electricity. In North America, AC electricity from a wall socket has a frequency of 60 Hz.
A coil turning in a magnetic field can also be used to generate DC power. A DC generator uses the same kind of split-ring commutator used in a DC motor. Unlike the AC generator, the polarity of the voltage generated by a DC generator is always the same. In a very simple DC generator with a single rotating loop, the voltage level would constantly fluctuate. The voltage from many loops (out of synch with each other) is usually added together to obtain a relatively steady voltage.
Rather than using a spinning coil in a constant magnetic field, another way to utilize electromagnetic induction is to keep the coil stationary and to spin permanent magnets (providing the magnetic field and flux) around the coil. A good example of this is the way power is generated, such as at a hydro-electric power plant. The energy of falling water is used to spin permanent magnets around a fixed loop, producing AC power.
You may have noticed that when something like a refrigerator or an air conditioner first turns on in your house, the lights dim momentarily. This is because of the large current required to get the motor inside these machines up to operating speed. When the motors are turning, much less current is necessary to keep them turning.
One way to analyze this is to realize that a spinning motor also acts like a generator. A motor has coils turning inside magnetic fields, and a coil turning inside a magnetic field induces an emf. This emf, known as the back emf, acts against the applied voltage that's causing the motor to spin in the first place, and reduces the current flowing through the coils. At operating speed, enough current flows to overcome any losses due to friction and to provide the necessary energy required for the motor to do work. This is generally much less current than is required to get the motor spinning in the first place.
If the applied voltage is V, then the initial current flowing through a motor with coils of resistance R is I = V / R. When the motor is spinning and generating a back emf, the current is reduced:
