13.4 The Magnetic Field of a Coil or Solenoid

Transcription

1 ection 13.3 Questions Figure 9 For question 3 1. An electric current is travelling southward in a straight, horizontal conductor. tate the direction of the magnetic field below the conductor above the conductor (c) east of the conductor (d) west of the conductor 2. What is the direction of the magnetic field lines around a conductor with the electric current travelling away from you, and toward you? 3. The diagram in Figure 9 represents two parallel current-carrying conductors. Determine whether the conductors attract or repel one another. Explain your reasoning. Reflecting 4. Why do you think the connection between electricity and magnetism was not discovered until the early 19th century? (Hint: Research when magnetism, static electricity, and current electricity were discovered.) 13.4 The Magnetic Field of a Coil or olenoid Figure 1 electromagnet: object that exerts a magnetic force using electricity solenoid: a coil of wire that acts like a magnet when an electric current passes through it uniform magnetic field: the magnetic field is the same strength and acts in the same direction at all points right-hand rule for a coil: If a coil is grasped in the right hand with the curled fingers representing the direction of electric current, the thumb points in the direction of the magnetic field inside the coil. In a junkyard, a crane lifts a pile of scrap metal to be compressed and eventually recycled (see Figure 1). How is the scrap metal held up by the crane? You might say by a magnet, but it couldn t be a permanent magnet otherwise how would the metal be released? It is held by an electromagnet, a device that exerts a magnetic force using electricity. The magnetic field around a straight conductor can be intensified by bending the wire into a loop, as illustrated in Figure 2. The loop can be thought of as a series of segments, each an arc of a circle, and each with its own magnetic field (Figure 2). The field inside the loop is the sum of the fields of all the segments. otice that the field lines are no longer circles but have become more like lopsided ovals (Figure 2). The magnetic field can be further intensified (Figure 3) by combining the effects of a large number of loops wound close together to form a coil, or solenoid. The field lines inside the coil are straight, almost equally spaced, and all point in the same direction. We call this a uniform magnetic field; the magnetic field is of the same strength and is acting in the same direction at all points. If the direction of electric current through the coil is reversed, the direction of the field lines is also reversed but the magnetic field pattern, as indicated by a pattern of iron filings, looks the same as it did before. To help you remember the relationship between the direction of electric current through a coil and the direction of the coil s magnetic field, there is the right-hand rule for a coil (Figure 4). Right-Hand Rule for a Coil If a coil is grasped in the right hand with the curled fingers representing the direction of electric current, the thumb points in the direction of the magnetic field inside the coil. 482 Chapter 13

2 13.4 electric current Figure 4 The right-hand rule for a coil Figure 5 shows the similarity between the magnetic fields of a bar magnet (Figure 5) and those of a coil (Figure 5). otice that the coil is wrapped around an iron core, which helps to increase the strength of the magnetic field. current flowing up Practice electric current Figure 5 The ends of a coil can be thought of as an -pole and an -pole, and the field within the core resembles the field in the interior of a bar magnet, with its ferromagnetic dipoles aligned so that they all point in the same direction. iron core Figure 2 current flowing down 1. Copy Figure 6 into your notebook and indicate on each diagram the direction of the electric current, the magnetic field lines around the coil, and the north and south poles of the coil. Figure 6 Figure 3 At both ends of the coil, the field is still strong, but along the sides, the magnetic field is weaker, as the field lines begin to bend and spread out. 2. If two identical cardboard tubes are wound with wire in exactly the same way and placed end-to-end with current passing through them in the same direction, will the two tubes attract or repel each other? Explain. Electromagnetism 483

3 Activity Magnetic Field of a Coil Question What are the characteristics of the magnetic field of a coil? Figure 7 etup for Activity One of the wires from the conductor should be connected firmly to one of the terminals; the other wire should be touched momentarily to the other terminal. The resistance of the bare wire is very low. As a result, it draws a large current. This will cause the wire to get hot and the battery to discharge quickly if the terminals are connected for too long a time. Be careful not to get iron filings in your eyes. Wash your hands after handling iron filings. Materials 50 cm of bare 12-gauge copper wire wooden dowel (about 15 cm long 4 cm diameter) stiff cardboard and scissors battery (6 V 12 V) or DC power supply connecting wires with alligator clips iron filings 2 compasses Procedure 1. Make a coil by winding the bare copper wire around the dowel as many times as possible. pread the loops out so that they are about 0.5 cm apart. Remove the dowel. 2. Using scissors, cut a piece of cardboard to fit snugly into the core of the coil, as shown in Figure 7. Insert the cardboard into one end of the coil, and support the coil so that the cardboard is horizontal. 3. Connect one end of the coil to one of the terminals of the battery using a wire with an alligator clip. Connect another wire with a clip to the other end of the coil, but do not connect the wire to the battery. 4. Lightly sprinkle iron filings on the cardboard, both inside and outside the coil. Momentarily touch the loose wire to the other terminal of the battery, and tap the cardboard gently. Once the iron filings have assumed a pattern, disconnect the battery and sketch the pattern, including the coil. From the battery terminals you used, determine in which direction the electric current was moving through the coil, and mark the direction on your sketch. 5. Place the compasses on the cardboard, one at each end of the coil. Reconnect the battery and note the directions in which the compasses point. Add these directions to your sketch of the iron filings. 6. Without moving the compasses, reverse the connections to the battery. Make another sketch. how the direction in which the electric current is moving. Observations Describe the direction, shape, and spacing of the magnetic field lines in the core of the coil. What happens to these magnetic field lines at the ends of the coil? (c) Describe the magnetic field in the region at either side of the coil. (d) Compare the compass direction pattern obtained in step 5 to that obtained in step 6. Does the right-hand rule provide an adequate description of these patterns? Explain. 484 Chapter 13

4 13.4 Factors Affecting the Magnetic Field of a Coil A coil with an electric current flowing through it has a magnetic field that can be plotted in the same way as for a bar magnet; however, it can be much more useful than a bar magnet. A bar magnet is able to pick up small pieces of iron but it cannot release them, and its strength cannot be varied. A coil, on the other hand, has a magnetic field that can be turned on and off and altered in strength. The strength of a magnetic field is related to the degree of concentration of its magnetic field lines. To increase the strength of the magnetic field in a coil, you must increase the number of magnetic field lines or bring them closer together. The magnetic field strength in a coil depends on the following factors. Current in the Coil ince the electric current flowing through the coil creates the magnetic field in the core of the coil, the more electric current there is, the greater the concentration of magnetic field lines in the core. In fact, in an air core coil (a coil with no material inside it), the magnetic field strength varies directly with the current in a coil: doubling the current doubles the magnetic field strength. umber of Loops in the Coil Each loop of wire produces its own magnetic field, and since the magnetic field of a coil is the sum of the magnetic fields of all its loops, the more loops that are wound in the coil, the stronger its magnetic field. Magnetic field strength varies directly as the number of loops per unit length in a coil: doubling the number of loops in a coil doubles the magnetic field strength. Type of Core Material The material that makes up the core of a coil can greatly affect the coil s magnetic field strength. For example, if a cylinder of iron rather than air is used as the core for a coil, the coil s magnetic field strength can be several thousand times stronger than with air. An aluminum core will have almost no effect on the strength. The core material becomes an induced magnet, as its atomic dipoles align with the magnetic field of the coil. As a result, the core itself becomes an induced magnet and the magnetic field strength increases. The factor by which a core material increases the magnetic field strength is called the material s relative magnetic permeability (K). The permeability is the ratio of the magnetic field strength in a material to the magnetic field strength that would exist in the same region if a vacuum replaced the material. K = magnetic field strength in material magnetic field strength in vacuum For example, a material with a relative magnetic permeability of 3 will make the field in a coil three times as strong as it would be in a vacuum. The magnetic field strength of a coil varies directly as the permeability of its core material: doubling the relative magnetic permeability of the core doubles the magnetic field strength. relative magnetic permeability: (K ) the factor by which a core material increases the magnetic field strength that would exist in the same region if a vacuum replaced the material Electromagnetism 485

5 paramagnetic: material that magnetizes very slightly when placed in a coil and increases the field strength by a barely measurable amount diamagnetic: materials that cause a very slight decrease in the magnetic field of a coil DID YOU KOW? Applying Paramagnetism and Diamagnetism One of the uses of paramagnetism is to analyze the components of materials such as powders and glasses. This application is performed using electron paramagnetic resonance apparatus. An interesting use of diamagnetism is found in levitation devices, such as a frictionless bearing in which a diamagnetic material is used in conjunction with a ferromagnetic material. Ferromagnetism, Paramagnetism, and Diamagnetism Core materials are divided into three groups according to their relative magnetic permeability. As you have learned, ferromagnetic materials become strong induced magnets when placed in a coil; that is, they have very high relative magnetic permeability. Iron, nickel, cobalt, and their alloys are ferromagnetic. Paramagnetic materials magnetize very slightly when placed in a coil and increase the field strength by a barely measurable amount. As a result, they have a relative magnetic permeability only slightly greater than 1. Oxygen and aluminum are paramagnetic. Diamagnetic materials cause a very slight decrease in the magnetic field of a coil and, as a result, their relative magnetic permeabilities are slightly less than 1. Copper, silver, and water are diamagnetic. The crane in Figure 1 of this section uses a huge electromagnet to lift the car. The electromagnet has a ferromagnetic core that passes through the coil and almost completely surrounds it. When the electromagnet is activated the core becomes completely magnetized. When the electromagnet is deactivated the core loses its magnetism and the car is released. (Even when the current is completely shut off, the magnet will not lose all of its strength because the core becomes a temporary magnet.) ample Problem Calculate the effect on the strength of the magnetic field in a coil when each of the following separate changes is made: the current in the coil is increased from 2.0 A to 5.0 A; the number of loops in the coil is changed from 4400 to 1100; the length of the coil is unchanged; (c) the core is changed from steel with a relative magnetic permeability of to iron with a relative magnetic permeability of olution Magnetic field strength varies directly with current. magnetic field after change = 5. 0 A magnetic field before change 2. 0 A = 2.5 The magnetic field strength is 2.5 times as great. Magnetic field strength varies directly with number of loops per unit length. magnetic field after change = magnetic field before change 4400 = 0.25 The magnetic field strength is 0.25 times as great. (c) Magnetic field strength varies directly with permeability of core. magnetic field after change = magnetic field before change = 2.7 The magnetic field strength is 2.7 times greater. 486 Chapter 13

6 13.4 Practice switch: a device that is used to make or break an electric circuit 3. An electromagnet is able to exert a force of when lifting an object. The electromagnet has 1000 turns, a current of 1.5 A, and a material in the core with a relative magnetic permeability of What force will the electromagnet exert if the following changes are made, each considered separately? The current is increased to 6.0 A. The number of turns in the coil is increased to 1400 without increasing the length of the coil. (c) All of the above changes are considered simultaneously. Answers (c) battery switch Applications of Electromagnetism Many appliances, tools, vehicles, and machines use a current-carrying coil to create a magnetic field. In most cases, the magnetic field is used to cause another component to move by magnetic attraction. A few examples will illustrate how electromagnets are used. Lifting Electromagnet Large steel plates, girders, and pieces of scrap iron can be lifted and transported by a lifting electromagnet (Figure 8). A soft ferromagnetic core of high relative magnetic permeability is wound with a copper conductor. The ends of the coil are connected to a source of electric potential through a switch. Closing the switch causes an electric current in the coil, and the soft iron core becomes a very strong induced magnet. When the switch is opened and the electric current stops, the soft iron core becomes demagnetized and releases its load. A U-shaped core is often used, with a coil wrapped around each leg of the device. If the coils are wound in opposite directions, the legs become oppositely magnetized and the lifting ability of the magnet is doubled. soft iron core Figure 8 A lifting electromagnet spring soft iron core switch Electromagnetic Relay A relay is a device in which a switch is closed by the action of an electromagnet (Figure 9). A relatively small current in the coil of the electromagnet can be used to switch on a large current without the circuits being electrically linked. A pivoted bar of soft iron, called an armature, is held clear of the contact point by a light spring. There is no current in the left-hand circuit, and the lamp is off. When the switch is closed, there is a current in the right-hand circuit, and the soft iron U-shaped core becomes magnetized. The magnetized core attracts the armature and pulls it to the right until it touches the contact point, completing the circuit. ow there is a current in the left-hand circuit, and the lamp goes on. When the switch is opened, the electric current drops to zero, the core becomes demagnetized, and the armature is released. When the spring pulls the armature away from the contact point, current drops to zero in the left-hand circuit and the lamp goes off. If the contact points were on the opposite side of the armature from the electromagnet, the relay would operate in reverse. Closing the switch would then turn the left-hand circuit off, and vice versa. battery Figure 9 An electromagnetic relay soft iron armature contact point relay: a device in which a switch is closed by the action of an electromagnet armature: a pivoted bar of soft iron soft iron core Electromagnetism 487

7 spring soft iron armature contact adjusting screw contact switch bell battery soft iron core Electric Bell In an electric bell, a small hammer is attached to the armature. The armature is vibrated back and forth several times a second, striking a metal bell. Figure 10 shows the circuit that causes the armature to move. When a button is pushed, the switch is closed. An electric current flows through the contacts and the spring to the coils, and the soft iron cores become magnetized. The cores attract the iron armature, which moves toward the electromagnet, causing the hammer to strike the bell. As the hammer strikes the bell, the movement of the armature opens the contacts. The electric current stops flowing to the coils and the soft iron cores become demagnetized, releasing the armature. A spring pulls the armature back to re-establish contact, thereby completing the circuit, and the entire cycle begins again. mall sparks, evidence of charge jumping across the gap, can be observed at the contact points as the circuit is alternately completed and broken. Figure 10 An electric bell Try This Activity Testing an Electromagnet Perform an activity in which you can use an electromagnet to lift iron objects, such as washers. The coil of the electromagnet can be connected to a variable DC power supply. Remember not to leave the current flowing for more than a few seconds at a time. Test the electromagnet both with and without the core, and with various currents and numbers of loops. ummarize your findings in tabular form. Practice Answers (c) 90.0 (c) + Figure 11 For question 4 + (d) + 4. Figure 11 shows coils of wire wound on cardboard cylinders. Copy the diagrams into your notebook, and on each diagram mark the direction of electric current, the direction of the field lines at each end of the coil, and the -pole and -pole of the coil. 5. A coil with an iron core is used as an electromagnet. With 500 loops and a current of 1.5 A, it can exert a lifting force of What force will it be able to lift if the following changes are made? The current is increased to 3.0 A. The number of loops is increased to 750 without increasing the length of the coil. (c) Both the above changes are made together. 6. In both electromagnetic relays and doorbells, soft iron cores are used in the electromagnets. If a hard iron core is used, explain what would happen in a relay that is used to turn a light on and off an electric bell Making Connections 7. Describe some commercial or industrial applications in which electromagnets are better than permanent magnets. Describe some applications in which permanent magnets are better than electromagnets. 488 Chapter 13

8 UMMARY The Magnetic Field of a Coil or olenoid The magnetic field around a coil is the sum of the magnetic fields of each of its segments. The right-hand rule for a coil states that if a coil is grasped in the right hand with the curled fingers representing the direction of electric current, the thumb points in the direction of the magnetic field inside the coil. The magnetic field strength of a coil depends on the current in the coil, the number of loops in the coil, and the type of core material compass ection 13.4 Questions 1. Each empty circle in Figure 12 represents a compass near one end of a coiled conductor. Redraw the diagrams, label the ends of the coils or, and show the direction of the compass needle in each case. 2. Two soft iron rods are placed inside a coiled conductor as shown in Figure 13. Determine whether the rods will attract or repel each other when the switch is closed. 3. Is insulation necessary for the conducting wires of a tightly wound coil? Explain. 4. Determine the polarity of the poles of the electromagnet in Figure tate the relationship between the strength of the magnetic field of a coil or solenoid and: the amount of current in the coil the number of loops in the coil (c) the type of core material in the coil 6. A coil of 600 turns, wound using 90.0 m of copper wire, is connected to a 6.0-V battery and is just able to support the weight of a toy truck. If 200 turns are removed from the coil but the wire is uncoiled and left in the circuit, what battery voltage would be needed in order to support the truck? 7. Explain the series of events involved in the operation of a doorbell. 8. The circuit for an electric bell is just a slight variation of the circuit for an electromagnetic relay. How are the circuits the same? Describe how the circuits are different. Making Connections 9. Describe how to construct a very strong lifting electromagnet. 10. Find out more about the uses of diamagnetic and paramagnetic materials. Write a brief report on what you discover. Follow the links for elson Physics 11, GO TO (c) conductor Figure 12 For question 1 Figure 13 For question 2 Figure 14 For question 4 Electromagnetism 489