# INDUCED ELECTROMOTIVE FORCE (1)

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1 INDUCED ELECTROMOTIVE FORCE (1) Michael Faraday showed in the 19 th Century that a magnetic field can produce an electric field To show this, two circuits are involved, the first of which is called the primary circuit consisting of a battery, a switch, a resistor to control the current and a coil of several turns around an iron bar When the switch is closed a current flows through the coil, producing a magnetic field that is particularly intense within the iron bar The secondary circuit also has a coil wrapped around the same iron bar, and is connected to an ammeter There is no battery in the secondary circuit, and no direct physical contact between the two circuits The magnetic field in the iron bar links the circuits, and helps to ensure that the field experienced in the secondary is almost the same as that produced by the primary 1

2 INDUCED ELECTROMOTIVE FORCE (2) When the primary circuit s switch is closed, the magnetic field in the iron bar rises from zero to a finite amount The ammeter in the secondary coil deflects to one side briefly and then returns to zero As long as the current in the primary circuit is maintained at a constant value, the ammeter in the secondary will read zero If the switch in the primary is opened, the magnetic field decreases back to zero, and as a result the ammeter in the secondary deflects briefly in the opposite direction, and then returns to zero The current in the secondary circuit is zero as long as the current in the primary circuit, and therefore the magnetic field in the iron bar, is not changing Current flows in the secondary circuit while the current in the primary is changing. It flows in opposite directions depending on whether the magnetic field is increasing or decreasing The current in the secondary is called the induced current, and the changing magnetic field creates an induced emf The magnitudes of the induced current and induced emf are found to be proportional to the rate of change of the magnetic field the more rapidly the magnetic field changes, the greater the induced emf 2

3 INDUCED ELECTROMOTIVE FORCE (3) The changing magnetic field is caused by a changing current in the primary circuit An emf can be induced using a simple bar magnet and secondary circuit as shown Here the magnetic field is changed by simply moving a permanent magnet toward or away from a coil connected to an ammeter When the magnet is moved toward the coil, the meter deflects in one direction When it is pulled away, the meter deflects in the opposite direction But there is no induced emf when the magnet is held still 3

4 MAGNETIC FLUX (1) The previous slides showed how changing the strength of the magnetic field that passes through a coil can induce an emf It is not only the magnetic field strength that can be changed, but also the field s direction or the cross sectional area of the coil or the coil s orientation Such situations can be described in terms of the change of a single quantity the magnetic flux The magnetic flux is a measure of the number of magnetic field lines that cross a given area 4

5 MAGNETIC FLUX (2) Suppose a magnetic field crosses a surface area A at right angles The magnetic flux, Φ, is simply Φ = BA If the magnetic field is parallel to the surface (b), it is evident that no field lines cross the surface, hence Φ = 0 Generally only the component of B r that is perpendicular to a surface contributes to a magnetic flux In (c), the magnetic field crosses the surface at an angle θ relative to the normal It s perpendicular component is Bcosθ Thus for a general magnetic flux Φ Φ = BAcosθ Units: 1 weber = 1T.m 2 5

6 MAGNETIC FLUX: EXAMPLE Consider a circular loop with a 2.5cm radius in a constant magnetic field of 0.625T. Find the magnetic flux through this loop when its normal makes an angle at 0, 30, 60 and 90 with the direction of the magnetic field B r 6

7 FARADAY S LAW OF INDUCTION In his experiments, Faraday discovered that the secondary coil (slide 1) experiences an induced emf only when the magnetic flux through it changes with time Also the induced emf for a given loop is found to be proportional to the rate at which the flux changes with time, Φ/ t If there are N loops in a coil, each with the same magnetic flux, Faraday found that the induced emf, ε, is given by ε = -N Φ/ t = -N(Φ final -Φ initial )/(t final -t initial ) Above is known as Faraday s Law of The minus sign indicates that the induced emf opposes the change in magnetic flux The magnitude of induced emf is given by ε = N Φ/ t = N (Φ final -Φ initial )/(t final -t initial ) Notice that Faraday s Law gives the emf that is induced in a circuit or a loop of wire The current that is induced as a result of the emf depends on the characteristics of the circuit itself (e.g. resistance, etc.) 7

8 FARADAY S LAW OF INDUCTION: EXAMPLE A bar magnet is moved rapidly toward a 40 turn circular coil of wire. As the magnet moves, the average value of Bcosθ over the area of the coil increases from T to 0.450T in 0.25s. If the radius of the coil is 3.05cm, and the resistance of its wire is 3.55Ω, find the magnitudes of the induced emf and the induced current. v 8

9 FARADAY S LAW OF INDUCTION: APPLICATIONS (1) A dynamic microphone is a device that uses a stationary permanent magnet and a wire coil attached to a moveable diaphragm When a sound wave strikes the microphone, the diaphragm oscillates, which in turn moves the coil further or closer to the magnet This movement changes the magnetic flux through the coil, and in turn induces an emf Connecting the coil to an amplifier increases the magnitude of the induced emf to a large enough amplitude so that it can power a set of speakers This is the same principle as a seismograph, but here the oscillations are caused by earthquakes and the vibrations they send through the ground 9

10 FARADAY S LAW OF INDUCTION: APPLICATIONS (2) Electric guitars work in a similar way The pickup in an electric guitar is simply a small permanent magnet with a coil wrapped around it This magnet produces a field that is strong enough to produce a magnetisation in the steel guitar string, which is the moving part in the system When the string is plucked, the oscillating string changes the magnetic flux in the coil, inducing an emf that can be amplified 10

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