Magnetism and Magnetic Fields

Magnetism and Magnetic Fields
© 2014 Pearson Education, Inc.

Chapter Contents Magnets and Magnetic Fields
Magnetism and Electric Currents The Magnetic Force 6 terms © 2014 Pearson Education, Inc.

22-1: Magnets and Magnetic Fields
Objectives: Identify the defining characteristics of north and south magnetic poles. Determine the direction of the magnetic field at a given location. Describe Earth’s magnetic field. © 2014 Pearson Education, Inc.

Magnets and Magnetic Fields
The effects of magnetism have been known since antiquity. For example, a piece of naturally occurring iron-oxide mineral known as lodestone can behave just like a manufactured magnet. Your first direct experience with magnetism was probably a playful exploration of bar magnets and their properties. From such experiences, you know that the two ends of a magnet are different. Specifically, you learned that a bar magnet attracts or repels another bar magnet depending on which ends of the magnet are brought together. © 2014 Pearson Education, Inc.

One end of a magnet is referred to as its north pole and is labeled N. The other end of a magnet is its south pole, which is labeled S. The poles of a bar magnet are defined by suspending it from a string so that it is free to rotate like a compass needle. The end of a freely rotating bar magnet that points toward the north geographic pole of the Earth is the north-seeking pole, or simply the north pole. The opposite end of the magnet is the south-seeking pole, or simply the south pole. © 2014 Pearson Education, Inc.

An interesting aspect of magnets is that they always have two poles. You might think that if you broke a magnet in two, each of the halves would have just one pole. That's not what happens. Instead, breaking a magnet in half produces two new poles on either side of the break, as is illustrated in the figure below. © 2014 Pearson Education, Inc.

This behavior is different from that of electricity, in that the two types of charge (positive and negative) can exist separately. Physicists continue to look for a single magnetic pole, known as a magnetic monopole, but none has been found. If two magnets are brought together in such a way that their opposite poles approach each other, as in the figure below, the force each experiences is attractive. © 2014 Pearson Education, Inc.

Like poles brought together, as shown below, experience a repulsive force. Just as an electric charge creates an electric field, so too does a magnet create a magnetic field. A magnetic field is a vector force field that surrounds any magnetic material. © 2014 Pearson Education, Inc.

In addition to exerting force, a magnetic field also contains energy, just like an electric field. The greater the energy, the more intense the field. A magnetic field, which is represented with the symbol B, can be visualized using small iron filings sprinkled onto a smooth surface. In figure (a) on the next slide, for example, a sheet of glass is placed on top of a bar magnet. When iron filings are sprinkled onto the glass sheet, they align with the magnetic field in their vicinity. The pattern they form gives a good idea of the overall field produced by the magnet. © 2014 Pearson Education, Inc.

Notice that the filings are bunched together near the poles of the magnets in the previous figures. This is where the magnet field is most intense. This can be illustrated by drawing field lines that are close together to one another near the poles (see figure below). © 2014 Pearson Education, Inc.

In addition, the lines form closed loops that leave the magnet at the north pole and enter it at the south pole. As the previous figure indicates, the direction of a magnetic field at a given location is defined as the direction a compass needle would point if placed at that location. Because opposites attract, the north pole of a compass needle—the end with the arrowhead—points toward the south pole of the magnet. © 2014 Pearson Education, Inc.

Recall that that the direction in which a compass points at any given location is the direction of the magnetic field at that point. Since a compass can point in one direction at a given point, there must be only one direction for the magnetic field, B. If field lines were to cross, there would be two directions for B at the crossing point. As a result, magnetic field lines can never cross. © 2014 Pearson Education, Inc.

The common household refrigerator magnet provides an interesting example of a magnetic field. These magnets are composed of multiple narrow magnet strips of opposite polarity, as indicated in the figure below. © 2014 Pearson Education, Inc.

Earth, like many planets, produces its own magnetic field. In many respects, Earth's magnetic field is like that of a giant bar magnet, as illustrated in the figure below. © 2014 Pearson Education, Inc.

As the preceding figure indicates, there is a magnetic pole near each geographic pole of the Earth. In addition, the field lines are essentially horizontal (parallel to the Earth's surface) near the equator but enter or leave the Earth near the poles. Because the north pole of a compass points toward the north geographic pole of Earth, and because opposites attract, we can conclude that the north geographic pole of Earth is actually near the south pole of the Earth's magnetic field. This is shown in the figure on the previous slide. © 2014 Pearson Education, Inc.

The axis of the magnetic poles is not perfectly aligned with the rotational axis of the Earth. Instead, it is inclined at an angle that varies slowly with time. Presently, the magnetic axis is tilted away from the rotational axis by an angle of about 11.5°. Scientist know that Earth's magnetic field has reversed direction many times over the ages. The last reversal occurred about 780,000 years ago. There are signs that Earth may be preparing for another such reversal. © 2014 Pearson Education, Inc.

As magnetic fields go, Earth's is relatively weak. To make this quantitative, we note that magnetic field strength is measured in terms of a unit called the tesla (T). The tesla is named in recognition of the pioneering electrical and magnetic studies of the Croatian-born American engineer Nikola Tesla (1856–1943). A magnetic field of 1 T is rather large. In comparison, the magnetic field at the surface of Earth is roughly 5.0 x 10−5 T. Another commonly used unit for magnetism is the gauss (G), which is defined as 1 G = 10−4 T. © 2014 Pearson Education, Inc.

The gauss is not an SI unit. Even so, it finds wide usage because of its convenient magnitude. In terms of the gauss, Earth's magnetic field at its surface is approximately 0.5 G. The magnitudes of some typical magnetic fields are given in the table below. © 2014 Pearson Education, Inc.

As was mentioned previously, Earth's magnetic field reverses direction over geological time periods. These reversals have left a permanent record in the rocks of the ocean floors. The figure below shows that molten rock is being extruded from a mid-ocean ridge. © 2014 Pearson Education, Inc.

The extruded rock has no magnetization because of its high temperature. When the rock cools, however, it becomes magnetized in the direction of Earth's magnetic field. In effect, the direction of Earth's magnetic field becomes "frozen" in the solidified rock. As the seafloor spreads, and more rock is formed along the mid-ocean ridge, a continuous record of Earth's magnetic field is formed. If the Earth's field reverses at some point in time, the field in the solidified rock will record the fact. © 2014 Pearson Education, Inc.

At the microscopic level, the magnetic field of a magnet is due to the magnetic fields produced by electrons in its atoms. Each electron acts like a small bar magnet. In some materials the magnetic fields of the electrons cancel, leaving zero net magnetic field. In other materials—like iron, nickel, and cobalt—the magnetic fields of the electrons don't cancel, and the electrons in neighboring atoms tend to align with one another, producing a strong magnetic field. © 2014 Pearson Education, Inc.

The magnetic field of any magnetic material is broken up into regions in which the field points in different directions, as is indicated in the figure below. A region within a magnetic material where the electrons are aligned in the same direction is referred to as a magnetic domain. © 2014 Pearson Education, Inc.

Each domain has a strong magnetic field in a given direction. Different domains are oriented differently, however, so that the net effect may be small. The typical size of these domains is on the order of 10−4 cm to 10−1 cm. When an external magnetic field is applied to such a material, the magnetic domains that are pointing in the direction of the applied field tend to grow in size at the expense of the domains with different orientations. © 2014 Pearson Education, Inc.

Many small animals are known to have small magnetic crystals (magnetite) in their bodies. For example, some species of bacteria use magnetite crystals to help orient themselves with respect to Earth's magnetic field. Magnetite has also been found in the brains of bees and pigeons, where it is thought to play a role in navigation. It is even found in human brains, though its possible function there is unclear. © 2014 Pearson Education, Inc.

22-2: Magnetism and Electric Currents
Objectives: Determine the direction of the magnetic field around a current-carrying wire by using the right-hand rule. Calculate the magnitude of the magnetic field at a given point near a current-carrying wire. Determine the force between two current-carrying loops of wire. © 2014 Pearson Education, Inc.

Magnetism and Electric Currents
The connection between electricity and magnetism was discovered accidentally by the Danish scientist Hans Christian Oersted (1777–1851) in 1820. Oersted was giving a science lecture when he closed a switch and allowed a current to flow through a wire. He noticed that a nearby compass needle rotated rapidly when the switch was closed. With that simple observation, Oersted discovered that electric currents can create magnetic fields. © 2014 Pearson Education, Inc.

To visualize the magnetic field produced by a wire, consider a long, straight wire that carries a current, I. Shaking iron filings onto a sheet of paper that is pierced by the wire results in a circular pattern of filings centered on the wire (see figure (a) below). Clearly, the magnetic field "circulates" around the wire. © 2014 Pearson Education, Inc.

We can gain additional information about the magnetic field by placing a group of small compasses about the wire, as in figure (b) below. In addition to confirming the circular shape of the field lines, the compass needles show the field's direction. © 2014 Pearson Education, Inc.

As the figure indicates, to find the direction of the field, point the thumb of the right hand in the direction of the current, I. The fingers then curl in the direction of the magnetic field, B. © 2014 Pearson Education, Inc.

In some cases a magnetic field will point into or out of the page. This can be difficult to draw. Therefore, we establish the convention that the symbol ⊗ indicates that the magnetic field points into the page. The way to remember this is to think of a magnetic field vector as an arrow. At the end of the arrow are crossed feathers. Therefore, if you view a vector from behind, it looks like an X. © 2014 Pearson Education, Inc.

Similarly, if the arrow points out of the page, all you will see is the point at its tip. Thus, we represent a magnetic field vector pointing out of the page with the symbol ⊙, where the dot represents the tip of the arrow. These convections are applied in the following example. © 2014 Pearson Education, Inc.

Experiments show that the magnetic field produced by a current-carrying wire doubles if the current, I, doubles. In addition, the field doubles if the radial distance from the wire, r, is halved. These observations are summarized in one statement: The magnetic field produced by a current in a wire is proportional to the current and inversely proportional to the radial distance from the wire. © 2014 Pearson Education, Inc.

The magnetic field for a long, straight wire is given by the following equation: In this equation, µ0, is a constant called the permeability of free space. Its value is µ0 = 4π x 10−7 T·m/A © 2014 Pearson Education, Inc.

You’ve seen that a long, straight wire carrying an electric current produces a magnetic field. What happens if a straight wire is wrapped into a circular loop instead? Figure (a) below shows a wire loop connected to a battery producing a current in the direction indicated. © 2014 Pearson Education, Inc.

Using the magnetic field RHR, as shown in the figure, we see that the magnetic field points from left to right as it passes through the loop. Notice also that the field lines are bunched together within the loop, indicating that the field is intense there. The field lines are more widely spaced outside the loop, where the field is weaker. The most interesting aspect of the field produced by the current-carrying loop is its close resemblance to the field of a bar magnet, as is illustrated in figure (b) on the next slide. © 2014 Pearson Education, Inc.

When two loops with identical currents are placed next to one another, the force between loops will be similar to the force between two bar magnets pointing in the same direction (see figure below). © 2014 Pearson Education, Inc.

As you can see, the ghosted bar magnets would attract one another, since their opposite poles are near one another. Therefore, wires with currents in the same direction experience an attractive force. As figure (b) below indicates, wires with currents in opposite directions experience a repulsive force. © 2014 Pearson Education, Inc.

A solenoid is an electrical device in which a long wire is wound into a succession of closely spaced loops—forming a cylindrical coil of wire. A solenoid carrying an electric current produces an intense, nearly uniform magnetic field inside the loops, as indicated in the figure below. © 2014 Pearson Education, Inc.

For this reason, solenoids are commonly referred to as electromagnets. Notice that each loop of a solenoid carries a current in the same direction. It follows that the magnetic field between loops is attractive and serves to hold them tightly together. The magnetic field lines in the previous figure are tightly packed inside the solenoid but are widely spaced outside. In the case of a very long, tightly packed solenoid, the magnetic field is intense and uniform inside the solenoid. © 2014 Pearson Education, Inc.

If a solenoid has N loops and length L, the magnetic field inside the solenoid is given by the following equation: Notice that the result is independent of the cross-sectional area of the solenoid and that the field depends directly on the number of loops per unit length and on the current. © 2014 Pearson Education, Inc.

When used as an electromagnet, a solenoid has many useful properties. A solenoid produces a strong magnetic field that can be turned on or off at the flip of switch—unlike the field of a permanent magnet. The magnetic field of a solenoid can be intensified by filling the core of the solenoid with an iron bar. In such a case, the magnetic field of the solenoid magnetizes the iron bar, and its field adds to that of the solenoid. © 2014 Pearson Education, Inc.

Assignment P. 788 Questions 1-6 P. 795 Questions 14-18

22-3: The Magnetic Force Objectives:
Calculate the magnitude of the force exerted by a magnetic field on a moving charge. Determine the direction of the force exerted by a magnetic field on a moving charge. Determine the magnitude and direction of the force exerted by a magnetic field on a current-carrying wire. © 2014 Pearson Education, Inc.

The Magnetic Force A magnetic field exerts a force on a moving charge. Both the magnitude and the direction of this force have some rather interesting characteristics. Consider a magnetic field, B, that points from left to right, as indicated in the figure below. Suppose an object with a charge q moves through the region with velocity v, and the angle between v and B is θ. © 2014 Pearson Education, Inc.

The Magnetic Force Notice that the equation uses the magnitude of the charge, |q|, because we are calculating the magnitude of the force. The equation also shows that the magnitude of the force depends on several different factors. Two of these factors are the same as the electric force. The magnetic force depends on the charge of the object, q. The magnetic force depends on the magnitude of the field, in this case, the magnetic field, B. © 2014 Pearson Education, Inc.

The Magnetic Force However, the magnetic force also depends on two factors that do not affect the strength of the electric force: The magnetic force depends on the speed of the object, v. An object at rest experiences no force. The magnetic force depends on the angle θ between the velocity vector and the magnetic field vector. © 2014 Pearson Education, Inc.

The Magnetic Force It is important to note that an object must have a charge and must be moving if the magnetic field is to exert a force on it. Even then the force vanishes if the object moves in the direction of the field (that is, if θ = 0) or in the direction opposite to the field (θ = 180°). Maximum magnetic force is exerted when a charged object moves at right angles to the magnetic field, so θ = 90° and sinθ = 1. © 2014 Pearson Education, Inc.

The Magnetic Force The deflection of moving charges by a magnetic field is illustrated in the figure below. The image on the TV screen is produced by a beam of electrons that "paints" the picture on the screen by illuminating the appropriate pixels. When a magnet is held near the screen, the electrons in the beam are deflected by the magnetic force, resulting in a scrambled picture. © 2014 Pearson Education, Inc.

The Magnetic Force On a large scale, the northern lights—or aurora borealis—are produced in a similar way. Positive and negative particles, ripped apart from atoms on the Sun by extremely high temperatures, form a gas-like collection of ions referred to as a plasma. Plasmas can be thought of the fourth state of matter. Though a plasma is similar to a gas, the fact that it consists of electrically charged particles means that electric and magnetic fields have a great influence on its behavior. © 2014 Pearson Education, Inc.

The Magnetic Force For example, figure (a) below shows streams of plasma shooting up from a storm on the surface of the Sun. The plasma follows arching paths that trace out the magnetic lines of the Sun. © 2014 Pearson Education, Inc.

The Magnetic Force Plasma shot into space from the Sun in an event known as a coronal mass ejection forms what is known as a solar wind. When the solar wind encounters Earth's magnetic field, the charged particles are deflected by the magnetic force. As a result, these particles concentrate where the field is most intense—near the poles of Earth (see figure (b) below). © 2014 Pearson Education, Inc.

The Magnetic Force The particles excite atoms in the atmosphere, causing them to glow and thus producing the northern lights, shown in figure (c) below, as well as their southern cousins, the aurora australis. © 2014 Pearson Education, Inc.

The Magnetic Force If the velocity of a charged object is perpendicular to a magnetic field, the result is circular motion of the object. In the figure below, an object of mass m, charge +q, and speed v moves in a region with constant magnetic field, B, pointing out of the paper. © 2014 Pearson Education, Inc.

The Magnetic Force A mass spectrometer is a device that makes use of circular motion in a magnetic field to separate isotopes (atoms of the same element that have different masses). In a mass spectrometer, a beam of charged particles enters a region with a magnetic field perpendicular to the velocity (see figure below). © 2014 Pearson Education, Inc.

The Magnetic Force A charged object experiences a force when it moves across magnetic field lines. This is true whether it travels in a vacuum or inside a current-carrying wire. Thus, a wire carrying a current in a magnetic field experiences a magnetic force that is simply the sum of all the magnetic forces experienced by the individual charges moving within it. To see how the force on a current-carrying wire is related to the forces on the individual charges, consider a straight wire segment of length L with a current I flowing left to right, as shown in the figure on the next slide. © 2014 Pearson Education, Inc.

The Magnetic Force As the figure indicates, there is also a magnetic field B present. The conducting charges move through the wire with an average speed given by v = L/Δt © 2014 Pearson Education, Inc.

The Magnetic Force The direction of the force on a current-carrying wire is given by the magnetic force RHR; the only difference is that you start by pointing your right hand in the direction of the current, I. In the case illustrated in the figure below, the force points out of the page. © 2014 Pearson Education, Inc.

The Magnetic Force The fact that a current-carrying wire experiences a force when placed in a magnetic field is one of the fundamental discoveries that makes modern applications of electric power possible. In most of these applications, including electric motors and generators, the wire is shaped into a current-carrying loop. We will now examine what happens when a simple current-carrying loop is placed in a magnetic field. © 2014 Pearson Education, Inc.

The Magnetic Force The torque exerted by a magnetic field finds a number of useful applications. For example, if a needle is connected to a coil, as in the figure below, it can be used as part of a meter known as a galvanometer, which is a device used to measure current in a circuit. © 2014 Pearson Education, Inc.

The Magnetic Force As a current passes through a galvanometer's coil, a torque acts on it, causing it to rotate. The spring ensures that the angle of rotation is proportional to the current in the coil. Of even greater importance is the fact that magnetic torque can be used to power a motor. Electric current passing through the coils of a motor causes a torque that rotates the axel of the motor. Electric motors are used in everything from electric razors to hybrid cars. © 2014 Pearson Education, Inc.

Chapter 23 Contents Electricity from Magnetism
Electric Generators and Motors AC Circuits and Transformers 5 terms © 2014 Pearson Education, Inc.

23-1: Electricity From Magnetism
Objectives: Recognize that the induced emf in a circuit is proportional to the rate of change of the magnetic field. Define magnetic flux and calculate the magnetic flux through a surface. Identify the direction of an induced current. © 2014 Pearson Education, Inc.

Electricity from Magnetism
When Hans Oersted observed that an electric current produces a magnetic field, it was pure serendipity. In contrast, Michael Faraday (1791–1867), an English chemist and physicist, was aware of Oersted's results, and purposely set out to see if a magnetic field could produce an electric field. His ingenious experiments showed that such a connection does exist. Faraday found that a changing magnetic field produces an electric current, but a magnetic field that doesn’t change has no such effect. Faraday set out to study this type of behavior. © 2014 Pearson Education, Inc.

The following figure shows a simplified version of Faraday's experiment. As the figure indicates, two electric circuits are involved. The first, called the primary circuit, consists of a battery, a switch, a resistor, and a wire coil wrapped around an iron bar. © 2014 Pearson Education, Inc.

When the switch is closed on the primary circuit, a current flows through the coil, producing a strong magnetic field in the iron bar. The secondary circuit also has a wire coil wrapped around the same iron bar, and this coil is connected to an ammeter that detects any current in the circuit. There is no battery in the circuit, and no direct physical contact between the two circuits. What does link the circuits, instead, is the magnetic field in the iron bar. © 2014 Pearson Education, Inc.

When the switch is closed on the primary circuit, the magnetic field in the iron bar rises from zero to some finite amount, and the ammeter in the secondary coil deflects to one side briefly and then returns to zero. As long as the current in the primary circuit is maintained at a constant value, the ammeter in the secondary circuit gives a zero reading. If the switch on the primary circuit is then opened, so the magnetic field drops again to zero, the ammeter in the secondary circuit deflects briefly in the opposite direction and then returns to zero. © 2014 Pearson Education, Inc.

These observations can be summarized as follows: The current in the secondary circuit is zero as long as the magnetic field in the iron bar is constant. It does not matter whether the constant value of the magnetic field is zero or nonzero. When the magnetic field in the secondary coil increases, a current is observed to flow in one direction in the secondary coil. When the magnetic field in the secondary coil decreases, a current is observed to flow in the opposite direction. © 2014 Pearson Education, Inc.

It is important to note that the current in the secondary coil appears without any physical contact between the primary and secondary coils. For this reason, the current in the secondary coil is referred to as an induced current. The process of inducing an electric current in a circuit by using a changing magnetic field is known as electromagnetic induction. © 2014 Pearson Education, Inc.

Because an induced current behaves the same as a current produced by an electromotive force (emf) supplied by a battery, we say that the changing magnetic field creates an induced emf in the secondary circuit. As far as the circuit is concerned, the changing magnetic field has the same effect as a battery. Faraday observed that the magnitude of the induced emf is proportional to the rate of change of the magnetic field—the more rapidly the magnetic field changes, the greater the induced emf. © 2014 Pearson Education, Inc.

Any means of changing the magnetic field is as effective as changing the current in the primary. The figure below shows a demonstration of induced emf. In this case, there is no primary circuit; instead, the magnetic field is changed by simply moving a bar magnet toward or away from a coil connected to an ammeter. © 2014 Pearson Education, Inc.

When the magnet is moved toward the coil, the meter deflects in one direction; when it is pulled away from the coil, the meter deflects in the opposite direction. There is no deflection when the magnet is held still. Understanding electromagnetic induction requires a new concept—magnetic flux. The word flux basically means "flow." For example, the flux, or flow, of air through a window is directly related to the direction of the wind and the cross-sectional area of the window. © 2014 Pearson Education, Inc.

Similarly, magnetic flux is a measure of the number of magnetic field lines that pass through a given area. A magnetic field perpendicular to a surface gives a high flux, and the larger the surface area, the greater the flux. A magnetic field parallel to a surface gives zero flux. Figure (a) on the next slide shows a magnetic field B crossing a surface area, A, at right angles. © 2014 Pearson Education, Inc.

The magnetic flux, Ф, in this case is simply the magnitude of the magnetic field times the area: Ф = BA If the magnetic field is parallel to the surface—like wind blowing parallel to an open window—then no field lines cross through the surface. As figure (b) on the next slide shows, the magnetic flux in this case is zero: Ф = 0. © 2014 Pearson Education, Inc.

In general, only the component of B that is perpendicular to a surface contributes to the magnetic flux. The magnetic field in figure (c) crosses the surface at an angle θ relative to the normal. © 2014 Pearson Education, Inc.

Faraday found that the secondary coil experiences an induced emf only when the magnetic flux changes with time. In general, the rate at which the magnetic flux changes is defined as follows: rate of change of magnetic flux = change in magnetic flux/change in time = ΔФ/Δt If there are N loops in a coil, the induced emf is given by Faraday's law of induction: © 2014 Pearson Education, Inc.

A familiar example of Faraday's law in action is the dynamic microphone. This type of microphone uses a stationary magnet and a wire coil attached to a movable diaphragm, as illustrated in the figure below. Sound waves move a coil of wire in a microphone, changing the magnetic flux through the coil. The result is an induced emf that is amplified and sent to speakers. © 2014 Pearson Education, Inc.

Nature often reacts in a way that opposes change. For example, if you compress a gas, the pressure of the gas increases—and opposes the compression. A similar principle applies to induced electric currents. It is known as Lenz's law, and was first stated by Estonian physicist Heinrich Lenz (1804–1865). Lenz's law states that an induced current always flows in a direction that opposes the change that caused it. Lenz's law is the reason for the negative sign in Faraday's law. It indicates that the induced current opposes the change in magnetic flux. © 2014 Pearson Education, Inc.

If the north pole of the magnet approaches the loop, a current is induced that tends to oppose the motion of the magnet. To be specific, the current in the loop creates a north pole of a magnet. This produces a repulsive force acting on the magnet, opposing the motion. On the other hand, suppose the magnet is pulled away from the loop, as in figure (b) on the next slide. The induced current is in the opposite direction, creating a south pole and a corresponding attractive force—which again opposes the motion. © 2014 Pearson Education, Inc.

Assignment P. 806 Questions 35-37 P. 827 Questions 7, 9-10

23-2: Electricity Generators and Motors
Objectives: Explain how an electric generator operates. Explain how an electric motor operates. © 2014 Pearson Education, Inc.

Electric Generators and Motors
An electric generator is a device designed to convert mechanical energy to electrical energy. The mechanical energy used to drive a generator can come from many different sources. Examples include falling water in a hydroelectric dam, expanding steam in a coal-fired power plant, and a gasoline-powered motor in a portable generator. All generators use the same basic operating principle—mechanical energy moves a conductor through a magnetic field to produce a motional emf. © 2014 Pearson Education, Inc.

Rotating a wire loop or coil in a magnetic field to change the magnetic flux allows the electromagnetic induction process to continue indefinitely. Thus, rotating a coil of wire through a magnetic field is a way to transfer energy from mechanical motion to an electric emf and current. To see how this works, imagine a wire coil of area A located in the magnetic field between the poles of a magnet, as illustrated in the figure on the next slide. © 2014 Pearson Education, Inc.

As mechanical work rotates the coil with an angular speed ω, the emf produced in it is given by Faraday's law. In the case of a rotating coil, it can be shown that Faraday's law gives the following result: ε = NBA sinωt © 2014 Pearson Education, Inc.

A current-carrying loop in a magnetic field experiences a torque that tends to make it rotate. If such a loop is mounted on an axle, as shown in the figure below, the magnetic torque can be used to operate machinery. This device converts electric energy to mechanical work. A device that converts electric energy into mechanical energy is called an electric motor. © 2014 Pearson Education, Inc.

Instead of doing work to turn a coil and produce an electric current, as in a generator, an electric motor uses an electric current to produce rotation of a loop or coil, which then does work. An electric motor transforms energy from electric emf and current into mechanical motion. It follows that an electric motor is basically an electric generator run in reverse. © 2014 Pearson Education, Inc.

23-3: AC Circuits and Transformers
Objectives: Recognize that both the voltage and the current in an AC circuit have a sinusoidal dependence. Calculate the average power in an AC circuit. Explain how transformers can be used to step up or step down the voltage in an electrical system. Relate the voltage and current in the primary coil of a transformer to the voltage and current in the secondary coil. © 2014 Pearson Education, Inc.

AC Circuits and Transformers
Electricity comes in two types—direct current and alternating current. Each has benefits and drawbacks. Alternating current is particularly useful in the home, in part because it works so well with devices called transformers that change the voltage. A simplified AC circuit diagram for a lamp is shown in the figure on the next slide. The bulb is represented by a resistor with equivalent resistance R and the wall socket is shown as an AC generator, represented by a circle enclosing one cycle of a sine wave. © 2014 Pearson Education, Inc.

The voltage delivered by an AC generator is plotted in figure (a) below. Notice that the graph has the shape of a sine curve. In fact, the mathematical equation for the voltage is V = Vmax sin ωt © 2014 Pearson Education, Inc.

In household circuits, the angular frequency is ω = 2πf, with f = 60 Hz. The maximum voltage, Vmax, is the largest value of the voltage during a cycle. Because the voltage in an AC circuit depends on the sine function, we say that it has a sinusoidal dependence. The current in a resistor in an AC circuit is I = Imax sinωt The value of the maximum current is given by Ohm's law: Imax = Vmax/R © 2014 Pearson Education, Inc.

It is easy to forget that household electrical circuits pose potential dangers to homes and their occupants. Fortunately, there are many devices available to ensure electrical safety. Fuses—In the case of a fuse, the current in a circuit must flow through a thin metal strip enclosed within the fuse. If the current exceeds a predetermined amount (typically 15 A), the metal strip becomes so hot that it melts and breaks the circuit. Thus when a fuse "burns out," it is an indication that too many devices are operating on that circuit. © 2014 Pearson Education, Inc.

Circuit Breakers—Circuit breakers like the one in figure (a) below provide protection in a way similar to a fuse by means of a switch that incorporates a bimetallic strip. © 2014 Pearson Education, Inc.

When the bimetallic strip is cool, it closes the switch, allowing current to flow. When the strip is heated by a large current, however, it bends enough to open the switch and the stop the current. Unlike a fuse, which cannot be used after it burns out, a circuit breaker can be reset when the bimetallic strip cools and returns to its original shape. © 2014 Pearson Education, Inc.

Polarized Plugs—The first line of defense against accidental shock is the polarized plug (see figure (b) below), on which one prong is wider than the other prong. The corresponding wall socket will accept the plug in only one orientation, with the wide prong in the wide receptacle. The narrow receptacle of the outlet is wired to the high-potential side of the circuit; the wide receptacle is connected to the low-potential side, which is essentially at ground potential. © 2014 Pearson Education, Inc.

A polarized plug provides protection by ensuring that the case of an electrical appliance, which is connected to the wide prong, is at low potential. Furthermore, when an electrical device with a polarized plug is turned off, the high potential extends only from the wall outlet to the switch, leaving the rest of the device at zero potential. © 2014 Pearson Education, Inc.

Grounded Plugs—The next line of defense against accidental shock is the three-prong grounded plug shown in figure (c) below. In this plug, the rounded third plug is connected directly to ground when plugged into a three-prong receptacle. In addition, the third prong is wired to the case of an electrical appliance. © 2014 Pearson Education, Inc.

If something goes wrong within the appliance, and a high-potential wire comes into contact with the case, the resulting current flows through the third prong, rather than through the body of a person who happens to touch the case. GFCI Devices—A even greater level of protection is provided by a device known as a ground fault circuit interrupter (GFCI), shown in figure (d) below. © 2014 Pearson Education, Inc.

The basic operating principle of an interrupter is illustrated in the figure below. Notice that the wires carrying an AC current to the protected appliance pass through a small iron ring. When the appliance operates normally, the two wires carry equal amounts of current in opposite directions—in one wire the current goes to the appliance, and in the other the current returns from the appliance. © 2014 Pearson Education, Inc.

Each of the wires produces a magnetic field, but because their currents are in opposite directions, the magnetic fields are in opposite directions as well. As a result, the magnetic fields of the two wires cancel. If a malfunction occurs in the appliance— say a wire frays and contacts the case—current that would ordinarily return through the power cord may pass through the user's body instead and into the ground. © 2014 Pearson Education, Inc.

In such a situation, the wire carrying current to the appliance immediately produces a net magnetic field within the iron ring that varies with the frequency of the AC generator. The changing magnetic field in the ring induces a current in the sensing coil wrapped around ring, and the induced current triggers a circuit breaker in the interrupter. This cuts the flow of current to the appliance within a millisecond, protecting the user. © 2014 Pearson Education, Inc.

It is often useful to change the voltage from one value to another in an electrical system. For example, high-voltage power lines may operate at voltages as high as 750,000 V, but before the electric power can be used in homes it must be stepped down (lowered) to 120 V. In other situations voltages need to be stepped up. The electrical device that changes the voltage in an AC circuit is called a transformer. © 2014 Pearson Education, Inc.

A simple transformer is shown in the figure below. Here an AC generator produces an alternating current in the primary (p) circuit at the voltage Vp. The primary circuit includes a coil with Np loops wrapped around an iron core. The iron core intensifies and concentrates the magnetic flux and ensures, at least to a good approximation, that the secondary (s) coil experiences the same magnetic flux as the primary coil. © 2014 Pearson Education, Inc.

Divide turns in secondary coil by number in the primary Step down transformer: decreases voltage, but increases current Step up transformer: Increases voltage, decreases current © 2014 Pearson Education, Inc.

A transformer depends on a changing magnetic flux to create an induced emf in the secondary coil. If the current is constant—as in a DC circuit—there is no induced emf, and the transformer ceases to function. This is an important advantage that AC circuits have over DC circuits and one reason why most electrical power systems operate with alternating current. Transformers play an important role in the transmission of electrical energy from the power plants that produce it to the communities and businesses where it is used. © 2014 Pearson Education, Inc.

When electrical energy is transmitted over large distances, the resistivity of the wires that carry the current becomes significant. If a wire carries a current I and has a resistance R, the power dissipated as heat is P = I 2R. One way to reduce this energy loss is to reduce the current. A transformer that steps up the voltage of a power plant by a factor of 20 will at the same time reduce the current by a factor of 20, which reduces the power dissipation by a factor of 202 = 400. When the electricity reaches the location where it is to be used, step-down transformers lower the voltage to a level such as 120 V or 240 V. © 2014 Pearson Education, Inc.

Magnetism and Magnetic Fields

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Magnetism and Magnetic Fields

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