Chapter 27, 28 & 29: Magnetism & Electromagnetic Induction. Magnetic flux Faraday s and Lenz s law Electromagnetic Induction Ampere s law


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1 Chapter 27, 28 & 29: Magnetism & Electromagnetic Induction Magnetic flux Faraday s and Lenz s law Electromagnetic Induction Ampere s law 1
2 Magnetic Flux and Faraday s Law of Electromagnetic Induction We have seen that current carrying wire generates a magnetic field around itself. Lets look at the other side of the coin, Can a magnetic field generate an electric current? Induced Electromotive Force Magnetic Flux Faraday s Law of Induction Lenz s Law Mechanical Work and Electrical Energy 2
3 Induced Electromotive Force: Faraday s Experiments Michael Faraday (1831) found that when a bar magnet was moved towards a coil of wire that was connected to a sensitive galvanometer, the galvanometer gave a momentary deflection showing that an electric current had been induced. When the magnet was moved away from the galvanometer, the galvanometer deflected in opposite direction. No current was induced when the magnet was held stationary inside or outside the coil. The process of setting up a current in the coil of wire through the relative motion of magnet and the coil is called Electromagnetic Induction. Faraday found that the induced current and the emf depends on (i) the number of turns in the coil, (ii) the strength of the magnet (iii) the speed with which the magnet is moved towards or away from the coil (iv) the core of the coil, e.g. an iron core induces more current 3
4 Induced Electromotive Force Note the motion of the magnet in each image: Away Towards Stationary 4
5 Induced Electromotive Force Faraday s experiment: closing the switch in the primary circuit induces a current in the secondary circuit, but only while the current in the primary circuit is changing. Iron Bar 5
6 Induced Electromotive Force 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 magnitude of the induced current is proportional to the rate at which the magnetic field is changing. 6
7 Magnetic Flux Magnetic Flux (): The flux (d) of magnetic field passing through a small area da is defined as the product of the area and the NORMAL component of B through the area. Flux is a scalar quantity. The total flux through a larger area is simply the integral of small elemental components B B A B BA A Bcos BAcos d A A: is the surface area vector B da B da 7
8 Magnetic Flux Magnetic Flux is a measure of the number of magnetic field lines that cross a given area. BA Where is the angle between the normal to the area (loop) and magnetic field If the area is of some complicated shape and B is not uniform, the magnetic flux can be written as the integral of elemental components. d B da B da 0 Magnetic flux is used in the calculation of the induced emf. 8
9 Faraday s Law of Induction From a consideration of experiments involving the production of an induced emf in a coil by either a changing magnetic field or a changing current, Faraday developed the following law. Faraday s law: The emf induced in a circuit is equal to the rate of change of magnetic flux through the circuit. OR When ever the magnetic flux linked with any circuit changes an emf () is induced. i.e. The induced emf is proportional to the rate of change of magnetic flux and to the number of turns (N) in the circuit. Minus sign reminds us of the direction in which the induced emf or induced current acts  Lenz s law 9
10 Faraday s Law of Induction There are many devices that operate on the basis of Faraday s law of Electromagnetic Induction. An electric guitar pickup: Tape recorder:
11 Lenz s Law Lenz s Law: An induced current always flows in a direction that opposes the change that produced it. i.e. An induced emf gives rise to an induced current which sets up a magnetic field to oppose the original change in flux. Therefore, if the magnetic field is increasing, the magnetic field created by the induced current will be in the opposite direction; if decreasing, it will be in the same direction. v v 11
12 Magnetic field of Induced Current LENZ LAW Consider the case: Npole of a bar magnet being moved towards a coil As the Npole moves closer to the coil, more field lines pass through the coil, the magnetic flux changes and hence emf is induced. Magnetic field of magnet Magnetic field of magnet The induced current sets up a magnetic field to oppose the change in flux. It sets up a N pole on the left side of the coil to repel the Npole of the bar magnet, thus the field lines are opposite to that of bar magnet 12
13 Magnetic Flux and Induced emf Exercise: A T magnetic field passes through a circular ring of radius 3.1 cm at an angle of 16 with the normal. Find the magnitude of the magnetic flux through the ring. Exercise: A 0.25 T magnetic field is perpendicular to a circular loop of wire with 53 turns and a radius of 15 cm. If the magnetic field is reduced to zero in 0.12 s, what is the magnitude of the induced emf? 13
14 EMF Induced in a Moving Conductor Consider a conducting metal rod of length l sliding with speed v (towards right) over two horizontal wires placed in a magnetic field B. This conducting rod completes the circuit. As it slides, the magnetic flux increases, and a current is induced and the bulb lights up. The induced current sets up a magnetic force in the opposite direction to oppose the motion of the rod. This diagram shows the variables we need to calculate the induced emf. 14
15 EMF Induced in a Moving Conductor If the rod moves with a speed v, it travels a distance, dx = vdt, in time dt, thus the change in the area of loop, da = ldx = lvdt Induced emf: d dt B da dt B lvdt dt Blv Thus induced emf depends on the strength of the magnetic field and the speed and length of the conducting rod If the rod is to move at a constant speed, v, an external force must be exerted on it. This force should have equal magnitude and opposite direction to the magnetic force: 15
16 Mechanical Work and Electrical Energy The mechanical power delivered by the external force is: Compare this to the electrical power in the light bulb: Therefore, mechanical power has been converted directly into electrical power. This simple example of motional emf illustrates the basic principle behind the generation of virtually all the world s electrical energy. 16
17 EMF Induced in a Moving Conductor Questions: In the following set of experiments, a galvanometer is used to detect a current flow. Mark in the direction of the current or write zero if appropriate v v (i) Loop moving into a uniform field (iii) Loop moving out of a uniform field x x x x v (ii Loop moving through a uniform field v (iv) Field moving while loop is stationary 17
18 EMF Induced in a Moving Conductor (v) Loop and field both stationary Initial x x x x x x x x x Final (vi) Magnitude of field increasing with time, Loop stationary 18
19 EMF Induced in a Moving Conductor Question: Consider a rectangular conducting loop of dimensions 4 cm 2 cm moving at a constant speed of 2 cm/s through a uniform magnetic field of strength 0.5 T as shown. Sketch the variation of magnetic flux through the coil and the induced emf. 2 cm 4 cm 2 cm/s 8 cm Answer: In this question students must realise that as long as the loop is outside the field, there is no change in magnetic flux, thus emf is zero. When the loop starts to enter the field, magnetic flux changes. It changes for 2 s, as it requires 2 s for the loop to completely enter the magnetic field. Once the entire loop is in the field, there is no change in flux (Max flux) for the next 2 s, as it takes 2s for the leading edge of the loop to reach the end of the field. Once the loop starts to leave the field, the flux changes for the next 2 s 19
20 2 cm 4 cm 2 cm/s 8 cm (Wb) t (s) emf (V) t (s)
21 EMF Induced in a Moving Conductor Question: Repeat the previous problem with the following loop dimensions and field configurations: L = 5 cm, W = 2 cm, B =2T, v = 2 cm s 1 and R =0.2 2 cm 5 cm 2 cm/s 5 cm 5 cm 5 cm 21
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