Generators and motors are two of the most important applications of induced emf (magnetic inductance). A generator is something that converts mechanical energy to electrical energy. A motor does the reverse, it converts electrical energy to mechanical energy. Here I'll discuss two types of generators, and say a few words about motors.
The basic generator design consists of a loop of wire capable of rotating inside a uniform magnetic field (sketch similar to Figure 20.17). Let's determine the emf generated as the loop rotates. This discussion differs from the one presented in the text, to give you an alternative way of thinking about the situation.
The loop has dimensions a by l, and area A = al; the magnetic field is of magnitude B, and directed horizontally from left to right. Now we assume the loop is rotating with constant angular speed w, or frequency f = 2p / w. When the loop is at an angle q = wt from vertical, the flux through the loop is Fi = B A cos(wt), since q = wt is the angle between B and the normal to the plane of the loop. This means that a time Dt later, the loop is at an angle q' w(t + Dt). The flux through the loop is now Ff = B A cosw(t + Dt). The change in flux is
In a practical generator, the emf is conveyed out of the coil to an external circuit using a pair of rings and brushes (diagram). The resulting emf varies sinusoidally with time (sketch). This is type of voltage is called alternating current (ac). The voltage varies between a maximum value of emfmax = NBAw, and a minimum of emfmin = -NBAw.
By a clever change to the rings and brushes of the ac generator, we can create a dc generator, that is, a generator where the polarity of the emf is always positive. The basic idea is to use a single split ring instead of two complete rings. The split ring is arranged so that, just as the emf is about to change sign from positive to negative, the brushes cross the gap, and the polarity of the contacts is switched. The polarity of the contacts changes in phase with the polarity of the emf -- the two changes essentially cancel each other out, and the emf remains always positive. The emf still varies sinusoidally during each half cycle, but every half cycle is a positive emf (drawing, like Figure 20.18(b)).
A motor is basically a generator running in reverse. A current is passed through the coil, producing a torque and causing the coil to rotate in the magnetic field. Once turning, the coil of the motor generates a back emf, just as does the coil of a generator. The back emf cancels some of the applied emf, and limits the current through the coil.
A coil of area 0.10 m² is rotating at 60 rev/s with its axis of rotation perpendicular to a 0.20T magnetic field. (a) If there are 1000 turns on the coil, what is the maximum voltage induced in the coil? (b) When the maximum induced voltage occurs, what is the orientation of the coil with respect to the magnetic field?
(a) First we need the angular speed w = 2pf = wp(60 Hz) = 377 rad/s. emfmax = N B A w = (1000)(0.20T)(0.10m²)(377 rad/s) = 7500V.
(b) When the maximum induced voltage occurs, sinwt = 1.0, so wt = 90°. This is the angle between the normal to the loop and the magnetic field, so the plane of the coil is parallel to the magnetic field.