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Chapter Thirty Seven Notes: Electromagnetic Induction.

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1 Chapter Thirty Seven Notes: Electromagnetic Induction

2  While Oersted's surprising discovery of electromagnetism paved the way for more practical applications of electricity, it was Michael Faraday in England and Joseph Henry in the United States who gave us the key to the practical generation of electricity: electromagnetic induction. They discovered that a voltage would be generated across a length of wire if that wire was exposed to a perpendicular Magnetic field flux of changing intensity. Until their discovery, the only current-producing devices were voltaic cells, which produced small currents by dissolving expensive metals in acid. These were the forerunners of our present-day batteries.  An easy way to create a magnetic field of changing intensity is to move a permanent magnet next to a wire or coil of wire. Remember: the magnetic field must increase or decrease in intensity perpendicular to the wire (so that the lines of flux "cut across" the conductor), or else no voltage will be induced:

3  Faraday and Henry found that moving a conductor in a magnetic field (or by moving the magnet field near a stationary conductor) created a voltage. The wire must be part of an electrical circuit. Otherwise the electrons have no place to go. In other words, there is no electrical current produced with a wire with open ends. But if the ends are attached to a light bulb, to an electrical meter or even to each other, the circuit is complete and electrical current is created.

4 Faraday's Law  "The induced voltage in a coil is proportional to the product of the number of loops, the cross sectional area of each loop, and the rate at which the magnetic field changes within those loops.“  Relates induced voltage to # of turns of coil and rate of change of magnetic field.  Moving a magnet in a coil induces a voltage in the coil.  Induced voltage creates a magnetic field that opposes the motion of the magnet  Energy is conserved ◦ If coil has no load no work is done to move the magnet ◦ If coil has a load, work to move magnet = work done in load.

5 Generators & Alternating Current ◦ Converts mechanical energy to electrical energy ◦ Coil rotates in magnetic field ◦ Turbine  Mech. energy from falling water or steam

6  Simple Generator:  Whereas a motor converts electrical energy into mechanical energy, a generator coverts mechanical energy into electrical energy.  The generators shown above, and on the previous slide are considered simple generators. They consist of one or just a few coils of wire which rotate in a magnetic field. Complex Generators: The generators found in power plants are much more complex than the models shown above. Huge coils made up of many loops of wire are wrapped on an iron core, to make an armature much like the armature of a motor. This armature is connect externally to a device that obtains its energy from a paddle wheel, turned by water, steam, wind or some other source of energy.

7 The fact that an electric current is deflected in a magnetic field, which underlies the operation of a motor, and Faraday and Henry’s discovery of electromagnetic induction, which underlies the operation of a generator occurred 10 years apart. Both of these are based upon the same fact: Moving charges experience a force that is perpendicular to both their motion and the magnetic field they traverse. Alternating Current Motor

8 ELECTRIC MOTORS  You may be surprised to know that you already have an electric motor in your own car. Your ignition system uses a small electric motor to get your car started. In very early cars, this had to be done manually. A removable crank fit into the engine, and the driver would have to turn it to get the car started, acting as a human generator.

9  construction of a transformer includes a ferromagnetic core around which multiple coils, or windings, of wire are wrapped. The input line connects to the 'primary' coil, while the output lines connect to 'secondary' coils. The alternating current in the primary coil induces an alternating magnetic flux that 'flows' around the ferromagnetic core, changing direction during each electrical cycle. The alternating flux in the core in turn induces an alternating current in each of the secondary coils. The voltage at each of the secondary coils is directly related to the primary voltage by the turns ratio, or the number of turns in the primary coil divided by the number turns in the secondary coil. For instance, if the primary coil consists of 100 turns and carries 480 volts and a secondary coil consists of 25 turns, the secondary voltage is then: secondary voltage = (480 volts) * (25/100) = 120 volts

10  What makes transformers so useful is that if you change the number of turns from one side to the other, you change the voltage in the wire on the right! Transformers can change a high voltage to a lower one, or a low voltage to a higher one. The primary voltage (on the left) induces a magnetic field in the core, which creates the secondary voltage (on the right). Explaining how a transformer works When an electric current passes through a long, hollow coil of wire there will be a strong magnetic field inside the coil and a weaker field outside it. The lines of the magnetic field pattern run through the coil, spread out from the end, and go round the outside and in at the other end. These are not real lines like the ones you draw with a pencil. They are lines that we imagine, as in the sketch, to show the pattern of the magnetic field: the direction in which a sample of iron would be magnetized by the field. Where the field is strongest, the lines are most closely crowded.

11 The iron core of a transformer is normally a complete ring with two coils wound on it. One is connected to a source of electrical power and is called the 'primary coil'; the other supplies the power to a load and is called the 'secondary coil'. The magnetization due to the current in the primary coil runs all the way round the ring. The primary and secondary coils can be wound anywhere on the ring, because the iron carries the changes in magnetization from one coil to the other. There is no electrical connection between the two coils. However they are connected by the magnetic field in the iron core. With a hollow coil the lines form complete rings. If there is an iron core in the coil it becomes magnetized, and seems to make the field become much stronger while the current is on.

12  When there is a steady current in the primary there is no effect in the secondary, but there is an effect in the secondary if the current in the primary is changing. A changing current in the primary induces an e.m.f. in the secondary. If the secondary is connected to a circuit then there is a current flow.  A step-down transformer of 1,200 turns on the primary coil connected to 240 V a.c. will produce 2 V a.c. across a 10-turn secondary (provided the energy losses are minimal) and so light a 2 V lamp.  A step-up transformer with 1,000 turns on the primary fed by 200 V a.c. and a 10,000-turn secondary will give a voltage of 2,000 V a.c. The iron core is itself a crude secondary (like a coil of one turn) and changes of primary current induce little circular voltages in the core. Iron is a conductor and if the iron core were solid, the induced voltages would drive wasteful secondary currents in it (called 'eddy currents'). So the core is made of very thin sheets clamped together, with the face of each sheet coated to make it a poor conductor. The edges of the sheets can be seen by looking at the edges of a transformer core.

13  First let's look at a transformer that converts a low voltage to a high one. This is called a step-up transformer.  If you increase the number of turns on the right, the voltage coming off the transformer will increase in proportion.  Using the numbers in the example above, you can see that the right side has four times more turns. As a result, the voltage on the right has increased four times (from 100 V to 400 V). The voltage has been stepped up by a factor of four.  Because current is inversely proportional to voltage, you can see that stepping up the voltage pays a price... the current on the right is only a quarter of what it was on the left. Step-up transformers increase the voltage, but decrease the current. In our example above, the current went from 10 A to 2.5 A, a reduction of by a factor of four.

14  Now let's look at a transformer which reduces the voltage. This is called a step-down transformer.  If you decrease the number of turns on the right, the voltage coming off the transformer will decrease in proportion.  Using the numbers in the example above, you can see that the right side has one fifth the number of turns. As a result, the voltage on the right is only one-fifth as large. The voltage has been stepped down by a factor of five (1000 V down to 200 V).  Because current is inversely proportional to voltage, you can see that stepping down the voltage gives a bonus... the current on the right is five times what it was on the left. Step-down transformers decrease the voltage, but increase the current. In our example above, the current went from 2 A to 10 A, an increase by a factor of 5.

15  Almost all electrical energy sold today is in the form of alternating current because of the ease with which it can be transformed from one voltage to another.  All modern countries are crisscrossed with high-voltage transmission lines, which transport electrical power from generators at power plants to substations and ultimately consumers. Why are high voltages used? What are the advantages of alternating current (AC) versus direct current (DC)? How much energy is lost in transmitting electrical power over long distances? The main physics principle this topic addresses is electrical resistance.  Power is transmitted great distances at high voltages and correspondingly low currents, a process that otherwise would result in large energy losses owing to the heating of the wires. Power may be carried from power plants to cities at about 120,000 volts or more, stepped down to 2400 volts in the city, and finally stepped down again by a transformer to provide the 120 (240) volts used in household circuits.

16  The most fundamental electric and magnetic fields underlie both voltages and currents.  James Maxwell said that there is a second effect that is a counterpart to Faraday’s law where only the roles of the electric and magnetic fields are interchanged.  Faraday’s law states that an electric field is induced in any region of space in which a magnetic field is changing with time. The magnitude of the induced electric field is proportional to the rate at which the magnetic field changes. The direction of the induced electric field is at right angles to the changing magnetic field.  According to Maxwell: a magnetic field is induced in any region of space in which an electric field is changing with time. The magnitude of the induced magnetic field is proportional to the rate at which the electric field changes. The direction of the induced magnetic field is at right angles to the changing electric field.

17  Just as an electrical current induces a magnetic field so does a changing magnetic field cause current to flow in a conductor. Scientists call this property electromagnetic induction. It allows us to convert mechanical energy, the energy of motion, into electricity. The impact that this simple physical property has had on the modern world is incalculable. 

18  A changing magnetic field passing through a conductor causes a current to flow in the conductor. This current in turn induces a magnetic field. The induced magnetic field points in the opposite direction of the changing magnetic field, opposing the changing field. (This is called Lenz's Law.) The external field must be changing! The induced field opposes the change in the external field, not the field itself. If the field is not changing, there is nothing to oppose and there is no current.

19 Approximate Years in Use: Present Maximum Capacity: About 1TB

20  If you shake a charged rod you will produce electromagnetic waves. This is because the shaking charge can be considered an electric current.  A magnetic field surrounds an electric current and a changing magnetic field surrounds a changing electric current.  A changing magnetic field will induce a changing electric field and a changing electric field will induce a changing magnetic field  An electromagnetic wave is composed of vibrating electric and magnetic fields that regenerate each other.  The magnitude of each induced field depends not only on the vibrational rate but on the motion of the other field. ◦ The higher the speed the greater the magnitude of the field that is induced.

21 Physics: Electromagnetic Waves Field Theory Michael Faraday, James Clerk Maxwell  The greatest change in the axiomatic basis of physics - in other words, of our conception of the structure of reality - since Newton laid the foundation of theoretical physics was brought about by Faraday's and Maxwell's work on electromagnetic field phenomena. (Albert Einstein, 1931) Mutual inductance and self-inductance  Mutual inductance occurs when two circuits are arranged so that the change in current in one causes an emf to be induced in the other.  Imagine a simple circuit of a switch, a coil, and a battery. When the switch is closed, the current through the coil sets up a magnetic field. As the current is increasing, the magnetic flux through the coil is also changing. This changing magnetic flux generates an emf opposing that of the battery. This effect occurs only while the current is either increasing to its steady state value immediately after the switch is closed or decreasing to zero when the switch is opened. This effect is called self-inductance. The proportional constant between the self- induced emf and the time rate of change of the current is called inductance (L)

22 Maxwell's equations and electromagnetic waves  Maxwell's equations summarize electromagnetic effects in four equations. The equations are too complex for this text, but the concepts embodied in them are important to consider. Maxwell explained that electric and magnetic waves can be generated by oscillating electric charges. These electromagnetic waves may be depicted as crossed electric and magnetic fields propagating through space perpendicular to the direction of motion and to each other, as illustrated in Figure 3.3 Figure 3 An electromagnetic wave consists of perpendicular oscillating magnetic and electric fields.

23  When Maxwell (1876) used this field theory to assume that light was an Electromagnetic Wave, and then correctly deduced the finite velocity of light, it was a powerful logical argument for the existence of the electromagnetic force field, and that light was a wave like change in the field (electromagnetic radiation) that propagated with the velocity of light c through the ether. The Electromagnetic Spectrum: Although all of these waves are electromagnetic waves, at different wavelengths and frequencies, they all move at the same speed. The speed of light. This was another discovery of Maxwell.  Remember that the electric field lines and the magnetic field lines are always perpendicular to each other!


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