Magnetic Fields 24 and Forces This detailed image of the skeletal system of a dolphin wasn’t made with x rays; it was made with magnetism. How is this done? LOOKING AHEAD ▶▶ Goal: To learn about magnetic fields and how magnetic fields exert forces on currents and moving charges. Magnetic Fields Sources of the Field Effects of the Field A compass is a magnetic dipole. It will Magnets produce a magnetic field; so do Magnetic fields exert forces on moving rotate to line up with a magnetic field. current-carrying wires, loops, and coils. charged particles and electric currents. You’ll learn how to use compasses and other You’ll learn to describe the magnetic fields created You’ll see how the motion of charged particles tools to map magnetic fields. by currents. These iron filings show the magnetic- in the earth’s magnetic field gives rise to the field shape for this current-carrying wire. aurora. LOOKING BACK ◀◀ Electric Fields In Chapter 20, we described electric STOP TO THINK interactions between charged objects in An electric dipole in a terms of the field model. uniform electric field u E experiences no net force, but it does experience a -q + q net torque. The rotation of this dipole will be You learned how to draw and interpret the electric field of a dipole. In this chapter, you’ll A. Clockwise. see how a magnetic dipole creates a magnetic B. Counterclockwise. field with a similar structure. KNIG9721_03_chap_24.indd 764 03/10/13 1:53 PM 24.1 Magnetism 765 24.1 Magnetism We began our investigation of electricity in Chapter 20 by looking at the results of simple experiments with charged rods. We’ll do the same with magnetism. Exploring magnetism Experiment 1 Experiment 3 North N If a bar magnet is taped to N N S a piece of cork and allowed S to float in a dish of water, N S it turns to align itself in an S approximate north-south South direction. The end of a mag- Cutting a bar magnet in half produces two weaker but still complete The needle of a magnets, each with a north pole and a south pole. net that points north is the WE N compass is a small north pole. The other end is magnet. S Experiment 4 the south pole. Magnets can pick up some objects, such S N A magnet that is free to pivot as paper clips, but not all. If an object is S attracted to one pole of a magnet, it is also like this is called a compass. Compass S N attracted to the other pole. Most materials, A compass will pivot to line up N S with a nearby magnet. S Bar magnet including copper, aluminum, glass, and N plastic, experience no force from a magnet. N Experiment 2 Experiment 5 Like poles repel: When a magnet is brought near an elec- SN N S troscope, the leaves of the electroscope remain undeflected. If a charged rod is N Unlike poles attract: brought near a magnet, there is a small S SN SN polarization force like the ones we studied in Chapter 21, as there would be on any If the north pole of one magnet is brought near the north pole of metal bar, but there is no other effect. No effect another magnet, they repel each other. Two south poles also repel each other, but the north pole of one magnet exerts an attractive force on the south pole of another magnet. What do these experiments tell us? ■ Experiment 5 reveals that magnetism is not the same as electricity. Magnetic poles and electric charges share some similar behavior, but they are not the same. ■ Experiment 2 shows that magnetism is a long-range force. Magnets need not touch each other to exert a force on each other. ■ Experiments 1 and 3 show that magnets have two types of poles, called north and south poles, and thus are magnetic dipoles. Cutting a magnet in half yields two weaker but still complete magnets, each with a north pole and a south pole. The basic unit of magnetism is thus a magnetic dipole. ■ Experiments 1 and 2 show how the poles of a bar magnet can be identified by using it as a compass. Other magnets can be identified by testing them against a bar magnet. A pole that repels a known south pole and attracts a known north pole must be a south magnetic pole. ■ Experiment 4 reveals that only certain materials, called magnetic materials, are attracted to a magnet. The most common magnetic material is iron. Magnetic materials are attracted to both poles of a magnet. STOP TO THINK 24.1 Does the compass needle rotate? N A. Yes, clockwise. B. Yes, counterclockwise. S Positively Pivot C. No, not at all. charged rod KNIG9721_03_chap_24.indd 765 03/10/13 1:53 PM 766 CHAPTER 24 Magnetic Fields and Forces 24.2 The Magnetic Field When we studied the electric force between two charges in ◀◀ SECTION 20.4, we devel- oped a new way to think about forces between charges—the field model. In this viewpoint, the space around a charge is not empty: The charge alters the space around it by creating an electric field. A second charge brought into this electric field then feels a force due to the field. The concept of a field can also be used to describe the force that turns a compass to line up with a magnet: Every magnet sets up a magnetic field in the space around it. If another magnet—such as a compass needle—is then brought into this field, the second magnet will feel the effects of the field of the first magnet. In this section, we’ll see how to define the magnetic field, and then we’ll study what the magnetic field looks like for some common shapes and arrangements of magnets. Measuring the Magnetic Field What does the direction a compass needle points tell us about the magnetic field at the position of the compass? Recall how an electric dipole behaves when placed in an electric field, as shown in FIGURE 24.1a. In Chapter 20 we learned that an electric dipole experiences a torque when placed in an electric field, a torque that tends to align the axis of the dipole with the field. This means that the direction of the electric field is the same as the direction of the dipole’s axis. The torque on the dipole is greater when the electric field is stronger; hence, the magnitude of the field, which we also call the strength of the field, is proportional to the torque on the dipole. The magnetic dipole of a compass needle behaves very similarly when it is in a magnetic field. The magnetic field exerts a torque on the compass needle, causing the needle to point in the field direction, as shown in FIGURE 24.1b. FIGURE 24.1 Dipoles in electric and magnetic fields. (a) Eu (b) Bu An electric A compass, a dipole rotates magnetic dipole, N to line up rotates so that its S with the north pole points electric eld. in the direction of the magnetic eld. Because the magnetic field has both a direction and a magnitude, we represent it using a vector. We will use the symbol Bu to represent the magnetic field and B to represent the magnitude or strength of the field. FIGURE 24.2 shows how to use a com- pass to determine the magnitude and direction of the magnetic field. The direction of the magnetic field is the direction that the north pole of a compass needle points; the strength of the magnetic field is proportional to the torque felt by the compass needle as it turns to line up with the field direction. FIGURE 24.2 Determining the direction and strength of a magnetic field. Magnetic eld here Weak eld: Needle points to upper right. turns slowly. SN SN Magnetic eld here Strong eld: Needle points to lower right. turns rapidly. KNIG9721_03_chap_24.indd 766 03/10/13 1:53 PM 24.2 The Magnetic Field 767 We can produce a “picture” of the magnetic field by using iron filings—very small elongated grains of iron. If there are enough grains, iron filings can give a very detailed representation of the magnetic field, as shown in FIGURE 24.3. The compasses that we use to determine field direction show us that the magnetic field of a magnet points away from the north pole and toward the south pole. FIGURE 24.3 Revealing the field of a bar magnet using iron filings. Each iron ling acts Since the poles of the like a tiny compass iron lings are not needle and rotates to labeled, a compass can point in the direction be used to check the of the magnetic eld. direction of the eld. S N Where the eld is strong, the torque Where the eld is easily lines up the weak, the torque barely lings. lines up the lings. Magnetic Field Vectors and Field Lines We can draw the field of a magnet such as the one shown in Figure 24.3 in either of FIGURE 24.4 Mapping out the field of a two ways. When we want to represent the magnetic field at one particular point, the bar magnet using compasses. magnetic field vector representation is especially useful. But if we want an overall The magnetic eld vectors point in the representation of the field, magnetic field lines are often simpler to use.