Now that you understand how magnetic fields are created, you need to understand how magnetic objects are affected by an external magnetic field. The situation is more complex than the electric field, where charges just follow the electric field lines. The effect of the magnetic field is rotational. To analyze how the magnetic field operates, you need some form of fundamental test particle. For the electric field, we use a point charge (i.e., a charged, infinitesimally small particle). Since magnetic charges do not exist, some alternative must be used. One such test particle is an infinitesimally small magnetic dipole. A magnetic dipole test particle can be thought of as a compass needle made exceedingly small.
A magnetic dipole has a north pole and a south pole, implying that it has direction in addition to magnitude. In other words, it is a vector
Figure 3.7 Magnetic field lines surrounding the earth.
Geographic North Pole (Magnetic South Pole)
Geographic South Pole (Magnetic North Pole)
quantity. The property of direction highlights a fundamental characteristic of the magnetic field that makes it different from the electric field. You know from experience that a compass needle always rotates so that the marked end (north pole) of the needle points north. If we place our conceptual compass in a magnetic field, the needle will likewise rotate until it points along the field lines. Its orientation will be such that its field lines up with those lines of the field in which it is immersed. So instead of a force being transmitted to the test dipole, torque is transmitted. A torque is the rotational analogy to a force. In this instance, the magnetic field acts as a "torque field" in comparison to the electric force field. This relation can be mathematically expressed as the following cross product:
t=m x b, where t is the torque in Newton-meters, m is the magnetic dipole moment in ampere-meters2, and B is the magnetic field in Webers/
FUNDAMENTALS OF MAGNETIC FIELDS Figure 3.8 The cross product right hand rule.
meter2. All three variables are vector quantities; that is, each has a magnitude and direction. The direction of the torque can be determined by the right hand rule for cross products, as shown in Figure 3.8. The magnitude of the torque is t = |mB sin(0), where 0 is the angle between the dipole, m, and the magnetic field, B. Motors
The electric motor is the most common method for converting electromagnetic energy into mechanical energy. Motors work from the principle of a rotating dipole. An example is the DC motor. The DC motor consists of the stator, which is the stationary enclosure, and the rotor, which is the rotating center that drives the axle. In its simplest form, the stator is a permanent magnet, which sets up a strong ambient magnetic field. The rotor is basically a coil of wire that forms a magnetic dipole when a DC current is driven through the wire. The rotor acts like a compass needle and moves to align its dipole moment with the magnetic field. To get the rotor to rotate continuously, some ingenious engineering is used. Just before the rotor completely aligns itself with the field, the DC current in the rotor is disconnected. The rotor's angular momentum causes it to freely rotate past alignment. Then the DC current is reconnected, but with reverse polarity. The rotor's dipole is consequently reversed, and the rotor is now forced to continue rotating another 180 degrees to try to align with the field. The process repeats ad nauseam. This simple example is called a two-pole motor because the rotor has two poles, north and south. More than one dipole can be used in a radial pattern on the rotor to produce a more powerful motor. You have now learned another way that electrical energy can be taken from a circuit. In Chapter 2, you learned that a resistor is just a device that converts electrical energy into heat. A motor converts electrical energy into mechanical energy. From the point of view of the circuit, this energy loss also appears as a resistance, although there is no "resistor" involved.
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