whole wheel, acting to slow it down. Since the magnitude of the countertorque is proportional to the angular velocity of the wheel, the braking
effect diminishes as the train slows, allowing it to come to a smooth stop. Eddy-current brakes are promoted as being quieter and less prone to
slippage than train brakes that rely on mechanical friction.
29.11 - Interactive problem: a generator
In this simulation your task is to establish how the angle between a magnetic field
and the velocity vector of a horizontal segment of a rotating loop relates to the emf
induced in the loop.
When you open the simulation by clicking on the diagram to the right, you will see a
loop of wire suspended in a magnetic field. Start the loop spinning by pressing GO.
An oscilloscope displays the emf induced in the loop. For simplicity’s sake, we omit
showing the oscilloscope’s connection to the generator circuit. We also show the
current induced in the visible portion of the circuit.
A black vector represents the tangential velocity of a horizontal loop segment. You
control how fast the loop rotates by setting its angular velocity. You can also change
the angle at which you view the simulation. The side view of the magnetic field is
particularly helpful for this exercise.
Watch the loop spinning in the field. Observe the orientation of the velocity vector to
the magnetic field lines. (The angle ș displayed in the control panel is the angle
between the field and the velocity vector as viewed from behind the crank.) With
what orientation of the velocity vector is the emf a maximum? A minimum? Can you explain why?
Also, observe the oscilloscope trace of the emf as the generator spins faster or slower. This always appears to be a sinusoidal wave. Does its
frequency change with angular velocity? Does its amplitude? To answer the second question, consider the relationship between speed and the
induced emf when a wire moves in a straight line through a magnetic field.
29.12 - An AC generator, its emf, and AC current
In this section, we consider the implications of adding an AC (alternating current)
generator to a circuit. We start with the circuit you see on the right, one that contains
only a generator and a resistor. The AC generator is represented by a blue circle with a
wave inside.
At its simplest, an AC generator consists of a wire loop that rotates in a magnetic field. It
generates an emf that varies sinusoidally with time.
The emf created by the generator can be described mathematically as the product of its
maximum emf and a sine function, as shown in Equation 1. The factor Ȧ in the
argument of the function is the angular frequency of the current. In the United States
and East Asia, alternating current has a frequency of 60 cycles per second (Hz),
meaning the emf reaches its maximum positive value 60 times per second. The
angular frequency is 2 ʌ times this value, about 377 rad/s.
In the United States, the maximum emf of alternating current is approximately 170 volts.
Utilities strive to provide a potential difference that, calculated in a specific way,
averages to 120 volts.