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Download unit 4 physics index book 1 — electric power
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UNIT 4 PHYSICS INDEX BOOK 1 — ELECTRIC POWER Magnetic Fields Page 1 Forces Experienced by Permanent Magnets Page 2 Magnetic Fields Produced by Moving Charges Page 3 Magnetic Fields Produced by Current in a Coil Page 5 Magnetic Forces on Moving Charges Page 7 Magnetic Forces on Current Carrying Conductors Page 9 DC Motors Page 14 Conductors Pushed Through Magnetic Fields Page 31 Magnetic Flux Page 33 Electromagnetic Induction Page 34 Induced EMF in a Straight Conductor Page 36 Generators Page 46 How Generators Differ from Motors Page 46 Calculation of EMF Page 46 Alternating Voltage and Current Page 54 Transformers Page 55 Power Transmission Page 59 Solutions AREA OF STUDY: ELECTRIC POWER MAGNETIC FIELDS A magnetic field can be thought of as a region in which magnetic forces exist. Such a field exists, for example, around a permanent magnet. Note that the magnetic field lines come out of the north pole of a magnet, and go into a south pole. Magnetic field lines represent the path that an imaginary North monopole would follow if it was placed in a magnetic field. As shown in the following diagram, a North monopole is repelled from the North pole of a magnet while being attracted to the South pole. Thus, the magnetic field, designated B, always points from North to South. The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 1 Draw field lines around the following pairs of magnets: FORCES EXPERIENCED BY PERMANENT MAGNETS The rule is simple: Unlike poles attract, like poles repel. S N S N The School For Excellence 2016 F F F F S N N S Master Classes – Unit 4 Physics – Book 1 Page 2 MAGNETIC FIELDS PRODUCED BY MOVING CHARGES When a current, I , flows through a wire, it produces a magnetic field around the wire. If the wire is straight, the magnetic field is cylindrical in shape: I W ire B The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 3 Use the Right Hand Grip Rule to determine the direction of the magnetic field: Imagine yourself gripping the wire: • The thumb is in the direction of the conventional current, I . • The fingers wrap around the wire in the direction of the magnetic field. For any given current, the magnetic field becomes weaker as distance from the wire increases. At any given distance from the wire, the magnetic field becomes stronger if I is increased. The unit of magnetic field strength is the tesla (symbol: T). Note: Magnetic field strength is sometimes referred to as magnetic flux density. One method of drawing three dimensional diagrams on a page is to use a series of crosses and dots to represent values going into or out of the page. This is a convention that can be used for all sorts of values, such as magnetic field and current. X X . = X . = into the page X . out of page . The following diagram demonstrates the layout of the magnetic field around a current carrying conductor. Test it with the RH grip rule. The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 4 MAGNETIC FIELDS PRODUCED BY CURRENT IN A COIL Use the Right Hand Grip Rule to determine the shape of the magnetic field produced by a current flowing around a coil. For example: Notice that in this example the magnetic field is directed into the page inside the coil and out of the page outside the coil. The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 5 Single coil Multiple coils (solenoid) Note that the pattern of magnetic field lines resembles the field around a bar magnet. Label the north and south ends of each coil. Some additional points to note: • The density of the magnetic field is greater inside the loop (or solenoid) than outside. • If many loops are placed side by side, their magnetic fields add together giving a much stronger effect. • The strength of the magnetic field can also be increased by increasing the current. • There is a near uniform magnetic field (i.e. parallel) inside the solenoid. • If an iron core is placed inside the solenoid the magnetic strength is increased significantly. Many aspects of the Area of Study on electric power require a clear understanding of magnetic fields, particularly electromagnets. The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 6 MAGNETIC FORCES ON MOVING CHARGES An electric charge that moves through a magnetic field experiences a force. This force is always perpendicular to both the magnetic field and the direction of motion of the charge. The charge need not be moving at right angles to the magnetic field but, if it is, then the force is at its maximum. Use the Right Hand Slap Rule to determine the direction of the vectors: • Thumb: Direction positive charges move (i.e. current) • Fingers: Magnetic field • Palm: Force on positive What would be the direction of force if electrons were used instead of positive charges? If the charge is moving parallel to the magnetic field, then the force = 0. The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 7 QUESTION 1 In 1898 Rutherford used a strong magnetic field to separate nuclear particles. The following information is given: Particle Alpha particle ( Beta particle 0 −1 e −1 γ 0 Gamma ray ( ( 0 0 4 2 He 2+ ) ) ) Mass Charge 6.640×10−27 kg 9.019×10−31 kg + 3.20×10−19 Coulomb − 1.60 ×10−19 Coulomb Zero Zero Discuss and show with a diagram, how a strong magnetic field could be used to separate these three particles. Have the particles project from left to right, and the magnetic field directed into the page. Solution The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 8 MAGNETIC FORCES ON CURRENT CARRYING CONDUCTORS Moving electric charges within magnetic fields experience a force. It therefore follows that a current carrying wire inside a magnetic field will also experience a force. If the wire is perpendicular to the magnetic field, then: F = BI l Where: F = Force experienced by the wire (newton, N) B = Magnetic field strength, or magnetic flux density (tesla, T) I = Electric current (ampere, A) l = Length of wire (metres, m) Note that: • l is the length of that part of the wire that is actually inside the B field. • F is always perpendicular to both B and the wire. Use the Right Hand Rule to determine directions: • Thumb: I • Fingers: B • Palm: F l I S N B S N F The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 9 The formula F = BIl only applies for the case where the wire is at right angles to the magnetic field. If the wire makes an angle θ to the B field, then: F = BIl sin θ . Even though this specific formula is not required for this course, its implications must be known: F = 0 if θ = 0, i.e. if the wire is in the same direction as B. F is maximum when θ = 90 o (since sinθ is maximum when θ = 90 o). When θ = 90o the equation F = BIl sin θ reduces to F = BIl . • • • QUESTION 2 (a) Find the magnetic force on a straight conductor whose length is 20 cm and carrying 3.0 A if it is situated in a vacuum and at right angles to a uniform magnetic field of strength 0.40 T. (b) If the conductor is rotated by 30° and again moved in the original direction, would the force on the wire be: A B C (c) Less than before? Same as before? More than before? With the conductor still rotated, would the direction of the force be the same or different to before? The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 10 Questions 3 and 4 refer to the following diagram: QUESTION 3 As shown in the diagram above, a current is flowing through a wire of length 2.0 m. A force of magnitude 0.008 N is acting on the wire. The wire is completely inside a magnetic field with a magnetic flux density of 0.8 T. The magnetic field is directed into the page. Calculate the current flowing in the wire. Give you answer in mA. Solution QUESTION 4 The direction of the force acting on the wire is: Solution The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 11 QUESTION 5 If a straight conductor is placed at right angles to a uniform magnetic field of 0.75 T and the force on a 2.0 m length of conductor is 0.75 N, calculate the magnitude of the current in the conductor. Solution QUESTION 6 What is the direction of the force acting on the current I? Solution The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 12 Two parallel conductors, A and B, have current flowing from left to right. What is the direction of the force that conductor A exerts on conductor B? In order to answer this question: 1. Select a point on conductor B, any point. 2. Determine the direction of magnetic field at this point. This field will be a result of the current running through conductor A (ignore conductor B as the net field here is zero). 3. Use the RH slap rule to determine the direction of the magnetic force. What if the conductors have current in opposing directions? Apply the same three-stage process and see what you come up with. The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 13 DC MOTORS Motors consist of a current carrying coil placed within a uniform magnetic field. The current is supplied by some external power supply (not shown in the following diagram). The coil is free to rotate. rotation axis F S S N P R B Q I S N F X Use the Right Hand Rule to determine the direction of the forces and thus the direction of rotation. In the diagram above we can clearly see that the force on side PS is upwards, and this force, in conjunction with the downward force on side QR, causes the coil to rotate in a clockwise direction. Use F = BIl to find the magnitude of F. If the coil has n turns, then the appropriate formula is: F = nBIl . The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 14 EXAMPLE 1 Two students attempt to construct a simple DC motor by making a square copper loop (ABYX), of side length 4.0 cm and 50 turns, connected to a power pack operating at 6.0 V and 1.5 A. Two magnets are suspended directly above and below the copper loop producing a magnetic field of strength 0.20 T. (a) Calculate the magnitude of the force on side AB. F = nBIl n = 50, l = 0.04 m, I = 1.5, B = 0.20 F = 50 x 0.20 x 1.5 x 0.04 F = 0.6 N (b) The direction of the force experienced by side AB is: A B C D E F G Left Right Up Down Into the Page Out of the page No force Answer is E. The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 15 (c) The direction of the force experienced by side BY is: A B C D E F G Left Right Up Down Into the Page Out of the page No force Answer is G. Why? (d) What is the magnitude of the net force on the coil? Net force is zero. What happens to the magnitude and direction of the force acting on side PS when the coil is rotated a quarter of a turn from the horizontal position shown? The following diagrams show that as the coil rotates the direction of the net force on side PS is still upwards. Side PS remains perpendicular to the field and current direction is unchanged. It follows that both the magnitude and direction of the force must be unchanged. The School For Excellence 2016 Master Classes – Unit 4 Physics – Book 1 Page 16