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Dunman High School (Senior High Physics Department) 9646 Physics (2014) Topic 16: Electromagnetic Induction 16-1 H2 Topic 16 Electromagnetic Induction Pickup of an electric guitar A moving coil speaker cone

Dunman High School (Senior High Physics Department) 9646 Physics (2014) Topic 16: Electromagnetic Induction 16-2 Learning Objectives Content  Magnetic Flux  Laws of Electromagnetic Induction Learning Outcomes Candidates should be able to a. define magnetic flux and the weber. b. recall and solve problems using  = BA. c. define magnetic flux linkage. d. infer from appropriate experiments on electromagnetic induction: i. that a changing magnetic flux can induce an e.m.f. in a circuit, ii. that the direction of the induced e.m.f. opposes the change producing it, iii. the factors affecting the magnitude of the induced e.m.f. e. recall and solve problems using Faraday’s law of electromagnetic induction and Lenz’s law. f. explain simple applications of electromagnetic induction.

Dunman High School (Senior High Physics Department) 9646 Physics (2014) Topic 16: Electromagnetic Induction 16-3 16.0 Introduction In Topic 15, you learnt two ways in which electricity and magnetism are related: i. an electric current produces a magnetic field ii. a magnetic field exerts a force on an electric current or moving electric charge. 16.1 Magnetic Flux Field lines tell us the strength and direction of the magnetic field. However, there are times where we will need to be able to calculate the amount of magnetic field that passes through a surface area. Hence, magnetic flux is the term used, and it is a measure of the number of field lines that pass through a given area A. Magnetic Flux passing through any surface area is defined as The product of the magnetic flux density and the area normal to the f ield through which the field is passing. For a uniform magnetic flux density B at an angle θ to an area A, the magnetic flux is given by Alternatively, we can view magnetic flux as the product of the component of B perpendicular to the surface and the area of the surface. ( ) Weber The SI unit of magnetic flux is the weber (symbol: Wb) which i s defined as the magnetic flux if a uniform magnetic flux density of 1 tesla passes perpendicularly through an area of 1 m2. (1 Wb = 1 T m2) 16.1.1 Magnetic Flux Linkage If the area A is bounded by a coil and the coil has N turns, then the total magnetic flux passing through the coil, otherwise known as magnetic flux linkage through the coil, is From the equation, magnetic flux linkage through a coil depends on i. number of turns in the coil N ii. magnitude of magnetic flux density B iii. the surface area A iv. the orientation of the coil  with respect to the direction of B. (Note:  is the angle between the magnetic flux density and the area of the coil) A change in any of these variables results in a change of magnetic flux linkage. Magnetic Flux Linkage Magnetic Flux Linkage is the product of the magnetic flux passing through the coil and the number of turns on the coil. Area, A θ Area, Asinθ B Magnetic flux through an area

Dunman High School (Senior High Physics Department) 9646 Physics (2014) Topic 16: Electromagnetic Induction 16-4 Example 1 The three loops of wire shown are all in a region of uniform magnetic field. Loop 1 swings back and forth as the bob on a pendulum, loop 2 rotates about a vertical axis and loop 3 oscillates vertically on the end of a spring. Which loop(s) have a magnetic flux that changes with time? Solution Only loop 2 has a changing magnetic flux as its orientation relative to the field changes as it rotates. Since the magnetic field is uniform, moving loop 1 back and forth or moving loop 3 up and down does not change the magnetic flux through the loop, that is, the magnetic flux does not depend on the loop’s position. Example 2 A coil of 10 turns and area 0.35 m 2 is placed perpendicular to a magnetic field of density 2.0 T as shown in the diagram on the left. Points P and Q are pulled apart until the coil becomes a straight line as shown in the diagram on the right. What is the change in magnetic flux linkage through the coil? Solution Initial magnetic flux linkage (N)i = NBA sin = 10(2.0)(0.35) sin 90°= 7.0 Wb Final magnetic flux linkage (N)f = 0 Change in magnetic flux linkage =(N)f  (N)i =  7.0 Wb Region of magnetic field Before After P Q P Q

Dunman High School (Senior High Physics Department) 9646 Physics (2014) Topic 16: Electromagnetic Induction 16-5 16.2 Electromagnetic Induction Ten years after the discovery that an electric current could produce a magnetic field, experiments conducted independently by Joseph Henry in United States and Michael Faraday in England showed that a changing magnetic field could induce an electric current in a circuit. The results of these experiments led to a basic and important law known as Faraday’s law. 16.2.1 Faraday’s Law Faraday’s Law of electromagnetic induction states that the induced e.m.f. is proportional to the rate of change of the magnetic flux linkage. If the magnetic flux linkage is measured in weber -turns and the e.m.f . in volts, then the constant of proportionality is unity. Mathematically: ( ) The negative sign is involved with the direction of the e.m.f. and is explained as part of the Len’z law. 16.2.2 Lenz’s Law Lenz’s Law states that the induced current or e.m.f. is in a direction so as to produce effects which oppose the change that is producing it. With the minus sign indicating that the induced e.m.f. opposes the change in magnetic flux linkage. Replacing magnetic flux ( ) Hence the e.m.f. induced depends on quantities such as N number of coils, magnetic flux density B, area of coil A and angle  between B and A.

Dunman High School (Senior High Physics Department) 9646 Physics (2014) Topic 16: Electromagnetic Induction 16-6 Example 3 A square coil of side 5.0 cm lies perpendicular to a magnetic field of flux density 4.0 T. The coil consists of 200 turns of wire. i. What is the magnetic flux linkage through the coil? NΦ = BA sinθ = (200)(4.0)(0.050)2 (sin 90°) = 2.0 Wb ii. The coil is rotated through an angle of 90 o in 0.20 seconds. Calculate the magnitude of the average e.m.f. induced in the coil while it is being rotated. ( ) ( ) ( )( )( ) ( ) Example 4 Predict the direction of the induced current in the circular coil for each of the following cases: Action Direction of induced current Pulling the coil to the right out of a magnetic field pointing out of page If the coil is pulled out of the field, magnetic flux linkage through the coil decreases. The induced current will be in a direction to oppose this decrease and hence will flow counter-clockwise to produce a magnetic field pointing out of the page. Shrinking a coil in a magnetic field pointing into page Since the coil area gets smaller, the magnetic flux linkage through the coil decreases. Hence the induced current will be clockwise to produce its own magnetic field into the page to make up for this decrease in magnetic flux linkage.

Dunman High School (Senior High Physics Department) 9646 Physics (2014) Topic 16: Electromagnetic Induction 16-7 Action Direction of induced current Rotating the coil by pulling the left side towards us and pushing the right side in with the magnetic field pointing right to left. Initially, the flux through the coil is zero. When the loop is rotated, the