2. Introduction to Magnetism <ul><li>The first known magnet are the stoned exposed to earth’s magnetic field called Loadstones , discovered by early Greeks and Chinese. </li></ul><ul><li>Magnet are surrounded by a field of force called magnetic field . </li></ul><ul><li>The magnetic force, force exerted by magnets to magnetic materials is a force at distance, just like gravity and electric force. </li></ul><ul><li>One of the earliest applications of magnetism is the magnetic compass. </li></ul><ul><li>Diskette, ATM cards and some other storage device contain tiny bits of magnetic materials. Exposure to magnetic field would damage these devices. </li></ul>
3. Magnetic field of magnets <ul><li>The magnetic of a magnet has the greatest concentration on its two ends called poles . </li></ul><ul><li>Magnetic field line are drawn to be emanating from the north pole and terminates to the south pole . </li></ul>N S N S N S Bar Magnet Horseshoe Magnet C-shaped Magnet
4. continuation: <ul><li>The magnetic field lines is made up of infinite number of magnetic field vectors. Magnetic field vectors are drawn tangent to the magnetic field line. </li></ul><ul><li>This method of visualizing magnetic fields was proposed by Michael Faraday , who initially called magnetic field lines of force or line of induction . </li></ul>
5. continuation: N S Magnetic field Magnetic field
6. Rules in drawing magnetic field lines <ul><li>The direction of the tangent to a magnetic field line at any point gives the direction of the magnetic field vector at that point. </li></ul><ul><li>The spacing between the lines represents the magnitude of the magnetic field. </li></ul><ul><li>Magnetic field lines emanate from the north pole and terminate at the south pole. </li></ul>
7. Polarity of Magnet <ul><li>Similar poles repel and opposite pole attracts. </li></ul><ul><li>When a magnet is divided into two (or several parts), each part has its own north and south poles. </li></ul><ul><li>As far as the current theories of magnetism are concerned, there are no magnetic monopoles. </li></ul>
8. continuation: N N N S S S N N N S S S REPULSION REPULSION ATTRACTION
9. Definition of Magnetic Field <ul><li>Magnetic field is defined in terms of force it can exert on a charge particle, called magnetic force. </li></ul><ul><li>Magnetic force is a cross-product: </li></ul>Where: F = Magnetic force (Newton) q = charge (coulomb) v = velocity (m/s) β = Magnetic field (Tesla)
10. continuation: <ul><li>The magnitude of the magnetic force is: </li></ul><ul><li>The direction of the magnetic force can be determined using the right-hand rule . </li></ul>Where: θ is the angle between velocity and magnetic field.
11. Right-hand-rule: <ul><li>Long, straight Current: </li></ul><ul><ul><li>Grasp the wire with your right hand so that your thumb point in the direction of the current. The curled fingers of that hand point the direction of the magnetic field. </li></ul></ul><ul><li>Current loop: </li></ul><ul><ul><li>Grasp the loop so that the curled fingers of your hand point in the direction of the current; the thumb of that hand then point in the direction of the magnetic field. </li></ul></ul>
12. continuation: <ul><li>Magnetic force can only change the direction of the particle’s motion, not its sound. </li></ul><ul><ul><ul><li>1 T = 1 kg/C-s </li></ul></ul></ul><ul><li>The SI unit of magnetic field ( β ) is Tesla (T). </li></ul><ul><li>A non-SI unit called gauss (G) is also used. </li></ul><ul><ul><ul><li>10 4 G = 1 T </li></ul></ul></ul>
13. Sample Problem: <ul><li>The velocity of an electron in a magnetic field of 2T is 4 x 10 5 m/s perpendicular to the field. Find the force that acts on the charge. </li></ul>
14. Magnetic Force <ul><li>Magnetic force on a current </li></ul><ul><ul><li>Since current, by definition are moving charge, current carrying conductors can also be moved by magnetic field. </li></ul></ul><ul><li>The magnetic force for a straight conductor in a uniform electric field. </li></ul>Where: F = magnetic force (Newton) I = current (ampere) L = Length of the conductor inside the magnetic field (meter) β = Magnetic field (Tesla)
15. continuation: <ul><li>The direction of the magnetic force is determined by right-hand-rule. </li></ul><ul><li>The magnitude of magnetic force is: </li></ul>Where: θ = is the angle between the wire and the magnetic field.
16. Sample Problem: <ul><li>A wire 0.10 m long carrying a current of 2.0 A is at 30 0 angle with respect to the magnetic field. If the magnetic field strength is 0.20 T, what is the magnitude of the force on the wire? </li></ul>
17. Magnetic field of Earth <ul><li>Magnetic north pole is located somewhere in the Greenland, near but not exactly in the same location as geographic north pole. Magnetic south pole is at its direct opposite. </li></ul><ul><li>Earth is the giant magnet that generates magnetic field. It enables compasses to work. </li></ul><ul><li>Earth magnetic north pole is actually the “south pole”, where magnetic field terminates, and the magnetic south pole is actually the “north pole” from where the magnetic field emanates. </li></ul>
18. continuation: <ul><li>Compasses: </li></ul><ul><ul><li>Instrument used to find direction. </li></ul></ul><ul><ul><li>Composed of slender bar magnet or low friction pivots. </li></ul></ul><ul><ul><li>Follow the magnetic field lines of the earth. </li></ul></ul><ul><ul><li>Point towards the geographic north pole. </li></ul></ul>
19. continuation: <ul><li>Earth Magnetosphere </li></ul><ul><ul><li>Region that contains a mix of electrically charged particles. </li></ul></ul><ul><ul><li>Electric and magnetic phenomena dominate rather than gravitational phenomena. </li></ul></ul><ul><ul><li>Shield earth from the solar wind is called bow shock. </li></ul></ul>
20. continuation: <ul><li>Van Allen Radiation Belts </li></ul><ul><ul><li>Traps high energy particles that leaked to magnetosphere. </li></ul></ul><ul><ul><li>Regions of particularly high concentration of charged particles. </li></ul></ul><ul><ul><li>Are responsible for the aurora (Northern and Southern Lights). </li></ul></ul>
21. Conductors with Current
22. Conductors with Current <ul><li>Electric current generate magnetic field. </li></ul><ul><li>Hans Christian Oersted noticed that the electric current can influence a compass needle. </li></ul><ul><li>Oersed and Andre-Marie Ampere shows that current carrying wires exert force to one another. </li></ul>
23. Straight Conductor <ul><li>The direction of the magnetic field in a straight conductor can be determined using the right-hand-rule . </li></ul>β I Conductor
24. Single-Loop Conductor <ul><li>The conductor maybe in the shape of circle, ellipse or polygon. </li></ul><ul><li>The magnetic field line’s direction must be according to the right-hand-rule with respect to the current. </li></ul>
25. continuation: <ul><li>The magnetic field vector at the center of the loop adds-up as one big magnetic field vector. </li></ul>I β
26. Solinoid <ul><li>Conducting wire coiled in the shape of helix. </li></ul><ul><li>Function like several adjacent single-loop conductor. </li></ul><ul><li>Similar to the wire coiled around an iron core (usually a nail) in an electromagnet. </li></ul>
27. <ul><li>The magnetic field vectors add-up at the center. </li></ul>continuation: C
28. <ul><li>An ideal solenoid is a solenoid of infinite length and uniform magnetic field inside the coil. </li></ul><ul><li>A real solenoid is a solenoid of limit length. Its magnetic field is uniform near the center but not uniform near the ends. </li></ul>continuation:
29. Moving Charged Particles
30. Moving Charged Particles <ul><li>All magnetic fields are generated by charging electric fields. </li></ul><ul><li>Moving charged particles generates electric field. Currents generate electric field because it is made-up of moving charge. </li></ul>+ - Positive charge : Use Right-Hand-Rule Negative charge : Use Left-Hand-Rule
31. <ul><li>If a charge is moving relative to a point, the electric field at that point due to the charge is changing. This on-going change generates magnetic field. </li></ul><ul><ul><li>Note: </li></ul></ul><ul><ul><li>Charging Electric field generates magnetic fields. </li></ul></ul>continuation: E 1 E 2 E 3 + + + + + + E 1 E 2 E 3
32. Calculating the Magnetic Field <ul><li>Biot-Savart Law </li></ul><ul><ul><li>Where: </li></ul></ul><ul><ul><ul><li>µ o = 4µ x 10 -7 Tm/A = 1.26 x 10 -6 Tm/A </li></ul></ul></ul>r d β I dl
33. continuation: <ul><li>Ampere’s Law </li></ul>r I dl
35. <ul><ul><li>Long cylindrical conductor of radius R </li></ul></ul><ul><ul><ul><li>Outside the conductor* Inside the conductor* </li></ul></ul></ul>continuation: R r Outside Inside I β
36. <ul><li>Circular loop of Radius r </li></ul><ul><ul><li>Center of a circular arc with central angle Ø (in Radian) </li></ul></ul>continuation: I r Ø
37. continuation: Complete circular loop I I r
38. continuation: <ul><ul><li>Distance z away directly above or below the center of circular loop. </li></ul></ul>z r I
39. continuation: <ul><li>Long solenoid (almost Ideal) with number of turns ( N ) per unit length. </li></ul><ul><ul><li>Inside the solenoid and near the center </li></ul></ul><ul><ul><li>Outside the solenoid </li></ul></ul>N
40. continuation: <ul><li>Sample Problem : </li></ul><ul><ul><li>Straight conductor : </li></ul></ul><ul><ul><li>What is the magnitude of the magnetic field 6.1 m below a power line in which there is a steady current of 100 A? </li></ul></ul><ul><ul><li>Field along a solenoid: </li></ul></ul><ul><ul><li>A solenoid of length 30.0 cm and radius 2.0 cm is closely winded with 200 turns of wire. The current in the winding is 5.0 A. Compute the magnetic field magnitude at a point near the center of the solenoid. </li></ul></ul>
41. Parallel Current <ul><li>The force between two parallel current I a and I b is given by: </li></ul><ul><ul><li>Where: </li></ul></ul><ul><ul><ul><li>L = Length of the conductors </li></ul></ul></ul><ul><ul><ul><li>d = distance between the conductors </li></ul></ul></ul>
42. continuation: <ul><li>The force is attractive if the currents are toward the same direction and repulsive if toward opposite directions. </li></ul>L I a I b d
43. Sample Problem: <ul><li>Parallel Currents </li></ul><ul><ul><li>Two long parallel wires are separated by distance of 8.0 cm. The current running along these wires are equal in magnitude but opposite direction. </li></ul></ul><ul><ul><li>What is the current along the wires if the magnitude field halfway between them is 300.0 N? </li></ul></ul><ul><ul><li>What is the force between the wires if the length of both of them is 4.0 m? Is this force attractive or repulsive? </li></ul></ul>
44. Magnetic Materials <ul><li>Atoms are like tiny magnets. The electrons form a microscopic loop. </li></ul>
45. <ul><li>Atoms are like tiny magnets. The electrons form a microscopic loop. </li></ul><ul><li>Moving electrons generate magnetic field. Hence, atoms are like small magnets. </li></ul><ul><li>Most objects do not generate magnetic field despite being made-up of atoms because the atoms are oriented randomly: the atoms cancel each other’s magnetic field. </li></ul>+ - I
46. Types of Magnetic Materials <ul><li>Paramagnetic </li></ul><ul><li>Ferromagnetic </li></ul><ul><li>Diamagnetic </li></ul>Assignment: Research “Types of magnetic materials” Computerized, Short Bond paper. To be submitted next meeting.
47. Field Symmetry <ul><li>Magnetic Flux defined </li></ul><ul><li>The magnetic flux ( Φ β ) is the strength of an electric field over an area in a field region. </li></ul><ul><ul><li>Where: </li></ul></ul><ul><ul><ul><li>β = Magnetic field (Tesla, T) </li></ul></ul></ul><ul><ul><ul><li>A = cross-sectional area (m 2 ) </li></ul></ul></ul><ul><ul><ul><li>θ = Angle </li></ul></ul></ul>
48. continuation: <ul><li>The term Magnetic flux density is synonymous to magnetic field, defined as the magnetic flux per unit of perpendicular area </li></ul><ul><li>The SI unit of magnetic flux is weber (Wb). </li></ul><ul><ul><li>1 Wb = 1 T*m 2 </li></ul></ul>N S
49. continuation: β β β β A A A β β
50. Conducting loop in a magnetic field <ul><li>Induction </li></ul><ul><ul><li>The process of producing current and emf by changing magnetic field. </li></ul></ul><ul><li>Induced current </li></ul><ul><ul><li>The current produced by changing magnetic field. </li></ul></ul><ul><li>Induced emf </li></ul><ul><ul><li>The work done per unit change in producing induced current. </li></ul></ul>
51. Note: Changing magnetic field generates electric field. N S continuation:
52. Law of Induction
53. Faraday’s Law <ul><li>States that the induced emf in a close loop equals the negative of the time rate of change of the magnetic flux through the loop. </li></ul>
54. continuation: <ul><li>Induced emf appears on the conducting loop if any of the following happens: </li></ul><ul><ul><li>The magnetic field is changing. </li></ul></ul><ul><ul><li>The area of the loop within the magnetic field is changing. </li></ul></ul><ul><ul><li>The conducting loop is rotating while immersed to magnetic field. </li></ul></ul>
55. Sample Problem: <ul><li>A single loop of wire with an enclosed area of 6.00 cm 2 is in a region of uniform magnetic field, with the field perpendicular to the plane of the loop. The magnetic field is decreasing at a constant rate of 0.150 T/s. </li></ul><ul><ul><li>What is the induced emf ? </li></ul></ul><ul><ul><li>If the loop has a resistance of 0.300 ohms what is the current induced in the loop? </li></ul></ul>
56. Lenz’s Law <ul><li>States that the induced current runs to the direction in such a way that it generates magnetic field to oppose the changes in the magnetic flux that induced the current. </li></ul>
57. continuation: <ul><li>Used in determining the direction of induced current and induced emf . </li></ul>S N β S N β S N β β ind β ind I = 0 I I (A) (B) (C) No motion β increasing in the loop β decreasing in the loop
58. Problem Solving: <ul><li>A rectangular inductor of unknown length and width of 0.2 m moves at 12 m/s to the right. It is oriented perpendicular to a magnetic field of 0.4 T. </li></ul><ul><ul><li>What is the induced emf in the circuit? </li></ul></ul><ul><ul><li>What is the direction of the induced emf? </li></ul></ul><ul><ul><li>If the resistance across the loop is 0.3 ohms, What is the current? </li></ul></ul>
59. Inductance <ul><li>Tendency of an electrical circuit to oppose the starting, stopping or changing the current. </li></ul><ul><li>Its SI unit is henry (H): </li></ul><ul><ul><li>1H = 1 Tm 2 /A </li></ul></ul>
60. Inductor <ul><li>Provides inductance in a circuit. </li></ul><ul><li>Produce uniform magnetic field. </li></ul><ul><li>The inductance L of an inductor with number of turns N is given by: </li></ul>
61. Problem Solving: <ul><li>A current of 5.0 mA passess through the solenoid inductor with 400 turns and inductance of 8.0 mH. What is the magnetic flux through the coil? </li></ul>
62. <ul><li>Self-inductance happens when two adjacent turns of a solenoid inductor induced one another to changing electric current. </li></ul><ul><li>The result of this is the intended function of the inductor: </li></ul><ul><ul><li>to resist changes in current. </li></ul></ul>Self-inductance
63. continuation: <ul><li>The self-induced emf is the emf that arises due to the turns in the inductor inducing one another: Self induced emf opposes the current. </li></ul>I I CURRENT DECREASING CURRENT INCREASING ε L ε L ε L ε L
64. continuation: <ul><li>The self-induced emf can be solved using the formula: </li></ul>
65. continuation: <ul><li>The inductance does not oppose the current itself, only the change in current. It opposes both increase and decrease in current. </li></ul>Inductance L Inductor If the current is increasing then the voltage Opposing that Change is created By the magnetic Field of the coil.
66. Mutual-Inductance (M) <ul><li>Proportionality between the emf generated in a coil to the change in current in the other coil which produces it. </li></ul><ul><li>Arises when to coils in close proximity induces emf to one another. </li></ul>
67. continuation: <ul><li>Notation: the subscript that the stand for the inducing coil comes second and the subscript that stands for the coil being induced comes first. </li></ul><ul><li>Equation of induced emf: ε 21 is the emf induced in coil 2 due to change in current in coil 1 and ε 12 is the emf induced in coil 1 cue to change in current in coil 2. </li></ul>
68. Sample Problem: <ul><li>Two single-turn coils are fixed in location such that they can induced emf to one another. </li></ul><ul><ul><li>When the first coil has no current and the current in the second coil increases at rate of 15.0 A/s, the emf in the first coil is 25.0 mV. What is their mutual inductance? </li></ul></ul><ul><ul><li>When the second coil has no current and the first coil has current of 3.60 A, What is the flux linkage in the second coil? </li></ul></ul>
69. Alternating Current <ul><li>Alternating current (ac) </li></ul><ul><ul><li>The current is not constant, but varies sinusoidally with time. </li></ul></ul>I t
70. <ul><li>Advantages over direct current (dc) </li></ul><ul><ul><li>Easier than transmit since charge carriers are not required to travel over long distance. </li></ul></ul><ul><ul><li>Enables transformers to work by utilizing Faraday’s Law of induction. </li></ul></ul><ul><ul><li>More readily adaptable to rotating machineries such as generators and electric motors. </li></ul></ul>continuation:
71. continuation: <ul><li>Alternating Current Generator </li></ul><ul><ul><li>The emf ε varies sinusoidally with time: </li></ul></ul><ul><ul><li>Driving frequency f d : </li></ul></ul>Where: W d = Angle of frequency of the emf t = time ε m = amplitude of the emf
72. continuation: <ul><li>The current I varies sinusoidally with time: </li></ul>
73. Oscillating Circuit
74. Resistive Load <ul><li>The phase constant is zero. </li></ul><ul><li>Time-varying voltage: </li></ul><ul><ul><ul><ul><li>Where: </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>V R = voltage across the resistor </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>V Rm = amplitude of the voltage </li></ul></ul></ul></ul></ul><ul><li>Time-varying current: </li></ul><ul><ul><ul><ul><li>Where: </li></ul></ul></ul></ul><ul><ul><ul><ul><li> I R = current through the resistor </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>I Rm = amplitude of the current </li></ul></ul></ul></ul></ul><ul><li>Relation of amplitude of current and voltage: </li></ul>R I I ε
75. Capacitive Load <ul><li>The phase constant is </li></ul><ul><li>Time-varying voltage </li></ul><ul><ul><ul><ul><li>Where: </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>V c = voltage across the Capacitor </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>V c m = amplitude of the voltage </li></ul></ul></ul></ul></ul><ul><li>Time-varying current: </li></ul><ul><ul><ul><ul><li>Where: </li></ul></ul></ul></ul><ul><ul><ul><ul><li> I c = current through the Capacitor </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>I c m = amplitude of the current </li></ul></ul></ul></ul></ul>C I I ε
76. continuation: <ul><li>Relation of amplitude of current and voltage: </li></ul><ul><li>The Quantity X C is called capacitive reactance: </li></ul><ul><li>The unit of reactance is ohms ( Ω ) </li></ul>
77. Inductive Load <ul><li>The phase constant is: </li></ul><ul><li>Time-varying voltage </li></ul><ul><ul><ul><ul><li>Where: </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>V L = voltage across the inductor </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>V L m = amplitude of the voltage </li></ul></ul></ul></ul></ul><ul><li>Time-varying current: </li></ul><ul><ul><ul><ul><li>Where: </li></ul></ul></ul></ul><ul><ul><ul><ul><li>I L = current through the inductor </li></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>I L m = amplitude of the current </li></ul></ul></ul></ul></ul>I I ε L
78. continuation: <ul><li>Relation of amplitude of current and voltage: </li></ul><ul><li>The Quantity X L is called inductance reactance: </li></ul><ul><li>The unit of reactance is ohms ( Ω ) </li></ul>
79. RLC Series Circuit <ul><li>The Resistor, Inductor and Capacitor are connected in series with ac emf device. </li></ul>ε L R C I I I I
80. continuation: <ul><li>Voltage and current in series circuit: </li></ul><ul><li>Relation of the amplitudes of voltage and current: </li></ul>
81. continuation: <ul><li>The quantity is called Impedance (Z): </li></ul><ul><li>The unit of reactance is ohms ( Ω ). </li></ul><ul><li>The phase constant can be solved using the equation: </li></ul>
82. Sample Problem: <ul><li>A 160 Ω resistor, 15.0 µF capacitor and 230 mH inductor are connected to form RLC circuit with an ac generator whose conducting loop rotates at 60.0 full rotation per second and with emf amplitude of 36.0 V. </li></ul><ul><li>Find: </li></ul><ul><ul><li>The impedance of the circuit. </li></ul></ul><ul><ul><li>The current flowing through the circuit. </li></ul></ul><ul><ul><li>The phase constant </li></ul></ul>
83. Transformer <ul><li>A device used to change the voltage and current levels in an AC circuit. </li></ul><ul><ul><li>Step-up transformer: V out > V in </li></ul></ul><ul><ul><li>Step-down transformer: V in > V out </li></ul></ul>
85. Characteristic of an Ideal Transformer <ul><li>Has two coil or windings, electrically insulated from each other but wound on the same core. </li></ul><ul><ul><li>Core typically made-up of material with large relative permeability such as iron. </li></ul></ul><ul><ul><li>Primary coil (input) – winding to which power supply is received. </li></ul></ul><ul><ul><li>Secondary coil (output) – winding to which power is delivered. </li></ul></ul><ul><li>Resistance is negligible. </li></ul><ul><li>Magnetic field is confined to the iron core. </li></ul>
86. Transformation of voltage and current <ul><li>The induced emf in primary, ε 1 , and secondary coil, ε 2 are: </li></ul><ul><li>We can combine the equation above as: </li></ul>
87. continuation: <ul><li>Terminal voltage of primary and secondary coil: </li></ul><ul><li>Step-up transformer, ε 2 > ε 1 and N 2 > N 1 </li></ul><ul><li>Step-down transformer, ε 1 > ε 2 and N 1 > N 2 </li></ul>
88. continuation: <ul><li>Power of Transformer: </li></ul><ul><li>If we place a resistance, R, to complete the circuit in the secondary coil: </li></ul>
89. Problem Solving: <ul><li>A transformer has 100 turns on its primary coil and 300 turns on the secondary coil. If the primary voltage is 110.0 V and primary current is 5.00 A. What are the secondary voltage and current? </li></ul>