14 Electromagnetism Chapter Topics Covered in Chapter 14 14-1: Ampere-turns of Magnetomotive Force (mmf) 14-2: Field Intensity (H) 14-3: B-H Magnetization Curve 14-4: Magnetic Hysteresis 14-5: Magnetic Field around an Electric Current © 2007 The McGraw-Hill Companies, Inc. All rights reserved.

Topics Covered in Chapter 14 14-6: Magnetic Polarity of a Coil 14-7: Motor Action between Two Magnetic Fields 14-8: Induced Current 14-9: Generating an Induced Voltage 14-10: Relays McGraw-Hill © 2007 The McGraw-Hill Companies, Inc. All rights reserved.

14-1: Ampere-turns of Magnetomotive Force (mmf) The strength of a coil’s magnetic field is proportional to the amount of current flowing through the coil and the number of turns per given length of coil. Ampere-turns = I × N = mmf I is the amount of current flowing through N turns of wire. This formula specifies the amount of magnetizing force or magnetic potential (mmf).

14-1: Ampere-turns of Magnetomotive Force (mmf) The SI abbreviation for ampere-turn is A · t. The cgs unit of mmf is the gilbert, abbreviated Gb. 1 A.t = 1.26 Gb Fig. 14-1: Two examples of equal ampere-turns for the same mmf. (a) IN is 2 × 5 = 10. (b) IN is 1 × 10 = 10. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-2: Field Intensity (H) The length of a coil influences the intensity of a magnetic field. Intensity is different from mmf. Equation: H = mmf/length Units: A·t/m ampere-turns per meter A·t/m is the mks unit The cgs unit for H is the oersted (Oe), which equals 1 gilbert per centimeter. Shorter magnetic circuits produce a greater field intensity

14-2: Field Intensity (H) The field intensity in the core is inversely related to length. Fig. 14-2: Relation between ampere-turns of mmf and the resultant field intensity H for different cores. Note that H = mmf/length. (a) Intensity H is 1000 A · t/m with an air core. (b) H = 1000 A · t/m in an iron core of the same length as the coil. (c) H is 100 / 2 = 500 A · t/m in an iron core twice as long as the coil. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-2: Field Intensity (H) Permeability (μ) Permeability is a measure of the ability to concentrate magnetic fields. Materials with high permeability can concentrate flux, and produce large values of flux density B for a specified H. The amount of flux produced by H depends on the material in the field. These factors are reflected in the formulas: B = μ × H μ = B / H

Permeability (μ) In cgs system, μ = 1 G/Oe for air or space i.e. B and H have the same value for air Relative permeability, μr is equal to absolute permeability B/H or μ In SI system, the permeability of air is μ0 = 1.26 x 10-6 So, μ = μ0 x μr = 1.26 x 10-6 x μr The unit is teslas per ampere-turn per meter:

14-2: Field Intensity (H) Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-3: B-H Magnetization Curve The B-H magnetization curve shows how much flux density B results from increasing field intensity H. Saturation is the effect of little change in flux density when the field intensity increases. Fig. 14-3: B-H magnetization curve for soft iron. No values are shown near zero, where μ may vary with previous magnetization. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-4: Magnetic Hysteresis Hysteresis refers to a situation where the magnetic flux lags the increases or decreases in magnetizing force. Hysteresis loss is energy wasted in the form of heat when alternating current reverses rapidly and molecular dipoles lag the magnetizing force. For steel and other hard magnetic materials, hysteresis losses are much higher than in soft magnetic materials like iron.

14-4: Magnetic Hysteresis Hysteresis Loop BR is due to retentivity, which is the flux density remaining after the magnetizing force is reduced to zero. Note that H = 0 but B > 0. HC is the coercive force (needed to make B = 0) Fig. 14-4: Hysteresis loop for magnetic materials. This graph is a B-H curve like Fig. 14-3, but H alternates in polarity with alternating current. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-4: Magnetic Hysteresis Demagnetization (Also Called Degaussing) To demagnetize a magnetic material completely, the retentivity BR must be reduced to zero. The practical way to do so is to magnetize and demagnetize the material with a decreasing hysteresis loop: A magnetic field is produced by alternating current. The magnetic field and the magnetic material are moved away from each other, or the current amplitude is reduced. The hysteresis loop then becomes smaller and smaller until it effectively collapses.

14-4: Magnetic Hysteresis Demagnetization (Also Called Degaussing) This method of demagnetization is called degaussing. Applications of degaussing include: Metal electrodes in a color picture tube Erasing the recorded signal on magnetic tape.

14-5: Magnetic Field around an Electric Current Straight Conductor A straight conductor can be a short but continuous length of conducting wire with no bends. A magnetic field is produced by the flow of current through a straight conductor. The magnetic field around a straight conductor is circular and perpendicular to the axis of the conductor. The polarity of the circular field is counterclockwise when viewed along the conductor in the direction of electron flow, Iin. These requirements apply to any charge in motion.

14-5: Magnetic Field around an Electric Current Clockwise and Counterclockwise Fields The left-hand rule for conductors: Grasp the conductor with your left hand so the thumb points in the direction of electron flow. Your fingers will encircle the conductor in the same direction as the circular magnetic field lines.

14-6: Magnetic Polarity of a Coil Bending a straight conductor into the form of a loop produces two effects: The magnetic field lines are more dense inside the loop. All the lines inside the loop aid in the same direction. This makes the loop field the same as a bar magnet, with opposite poles at opposite faces of the loop.

14-6: Magnetic Polarity of a Coil A coil of wire conductor with more than one turn is called a solenoid. To determine magnetic polarity for a solenoid, grasp the electromagnet with the left hand. When the fingers of the left hand curl around the turns of an electromagnet in the direction of electron flow, the thumb points to the north pole. The magnetic polarity depends on the direction of current flow and the direction of winding. The current is determined by the connections to the voltage source: flow runs from negative to positive.

14-6: Magnetic Polarity of a Coil Fig. 14-10: Left-hand rule for north pole of a coil with current I. The I is electron flow. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-7: Motor Action between Two Magnetic Fields Motor action is the result of two magnetic fields interacting with one another. The fields can attract or repel. Motion is produced from a stronger field toward a weaker field.

14-7: Motor Action between Two Magnetic Fields Current in a conductor has its own magnetic field. When placed in the magnetic field of a separate source, the two can produce motor action. The conductor must be perpendicular to the field. It must also be in the same plane. There is stronger force below the conductor, because the fields add up, so conductor moves up.

14-7: Motor Action between Two Magnetic Fields Fig. 14-13: Motor action of current in a straight conductor when it is in an external magnetic field. The HI is the circular field of the current The HM indicates field lines between the north and south poles of the external magnet. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-7: Motor Action between Two Magnetic Fields Torque is the effect of a force producing rotation. Torque is produced when opposing magnetic fields in a loop produce an upward force on one side of the loop and downward force on the other. Torque is the basis of all electric motors. Torque is proportional to current, so the amount of rotation indicates how much current flows through the coil.

14-8: Induced Current Generator Action When a moving conductor cuts across flux lines, a voltage is induced. The amount of induced voltage is proportional to: The conductor velocity The amount of flux The number of turns of wire The polarity of induced voltage is determined by Lenz’s law (discussed in section 14-9).

14-8: Induced Current Lenz’s law states that the direction of an induced current must be such that its own magnetic field will oppose the action that produced the induced current. The direction of the induced current is determined by the left-hand rule for electron flow. If the fingers coil around the direction of electron shown, under and over the winding, the thumb will point to the left for the north pole. Fig. 14-15: Induced current produced by magnetic flux cutting across turns of wire in a coil. Direction of I here is for electron flow. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-9: Generating an Induced Voltage Consider a magnetic flux cutting a conductor that is not in a closed circuit, as shown in Figure 14-16. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-9: Generating an Induced Voltage The motion of flux across a conductor in an open circuit forces free electrons to move. Since the ends are open, electrons accumulate at them, creating a potential difference. The potential difference is an electromotive force (emf), generated by the work of cutting across the flux. Induced emf increases with the number of turns in a coil. The polarity of the induced voltage follows from the direction of induced current.

14-9: Generating an Induced Voltage Faraday’s Law of Induced Voltage The amount of voltage induced by flux cutting the turns of a coil is determined by three factors: The amount of flux More voltage is generated by a stronger magnet. The number of turns Increasing the turns generates more voltage. The time rate of cutting. Less voltage is generated when the conductor moves slowly. Either the flux or the conductor can move.

14-9: Generating an Induced Voltage Faraday’s Law of Induced Voltage The amount of induced voltage can be calculated by Faraday’s law: N = number of turns dΦ/dt = how fast the flux cuts across the conductor. vind = N dΦ (webers) dt (seconds)

14-9: Generating an Induced Voltage Fig. 14-17: Voltage induced across coil cut by magnetic flux. (a) Motion of flux generating voltage across coil. (b) Induced voltage acts in series with coil. (c) Induced voltage is a source that can produce current in an external load resistor RL connected across the coil. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-9: Generating an Induced Voltage Fig. 14-18: Graphs of induced voltage produced by magnetic flux changes in a coil. (a) Linear increase of flux Φ. (b) Constant rate of change for dΦ/dt at 2 Wb/s. (c) Constant induced voltage of 600 V, for a coil with 300 turns. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-9: Generating an Induced Voltage Faraday’s Law of Induced Voltage The amount of induced voltage is calculated by Faraday’s law: The induced voltage is directly proportional to the number of turns times d/dt. To generate more voltage: Increase the number of turns Increase the flux Decrease the time vind = N d(Wb) dt(seconds)

14-9: Generating an Induced Voltage Polarity of Induced Voltage The polarity of induced voltage is determined by Lenz’s law. An induced voltage has the polarity that opposes the change causing the induction. Absolute polarity depends upon three points: Whether the flux is increasing or decreasing; The method of winding; Which end of the coil is the reference.

14-10: Relays A relay is an electromechanical device that operates on the basis of electromagnetic induction. It uses an electromagnet to open or close one or more sets of contacts. Relays, like switches, have poles and throws. Relays can switch or control high power loads with a low amount of input power. In remote-control applications, relays can control high power loads long distances away more efficiently than can mechanical switches.

14-10: Relays The switching contacts of a relay may be: Normally open (NO) Normally closed (NC) The movable arm on a relay is called the armature. When the coil is energized, the armature: Opens the contacts (NC relay) Closes the contacts (NO relay)

14-10: Relays An SPDT relay has both NO and NC contacts. When the coil is energized, the armature is attracted and opens the NC contacts and closes the NO contacts. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

14-10: Relays Relay Specifications: The following are a relay’s most important ratings: Pickup voltage The minimum amount of relay coil voltage necessary to energize or operate the relay. Pickup current The minimum amount of relay coil current necessary to energize or operate the relay. Holding current The minimum amount of current required to keep a relay energized or operating (less than the pickup current). Dropout voltage The maximum relay coil voltage at which the relay is no longer energized.

14-10: Relays Relay Specifications: Important ratings, cont. Contact voltage rating The maximum voltage the relay contacts are capable of switching safely. Contact current rating The maximum current the relay contacts are capable of switching safely. Contact voltage drop The voltage drop across the closed contacts of a relay when operating. Insulation resistance The resistance measured across the relay contacts in the open position.

There is continuity between the main contact and the NO contact. 14-10: Relays The pickup current is greater than the hold current because of the air gap. The armature has moved and the air gap is gone. Less current is now required to overcome the spring and hold the relay closed. There is continuity between the main contact and the NO contact. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.