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| Summary |
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 Electromagnetic induction (E.M.I) is the phenomenon of generating EMF by changing the number of magnetic lines of force associated with a circuit. The EMF so generated is called induced EMF and the corresponding current is called induced current. |
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| The number of magnetic lines of force crossing a surface is called magnetic flux linked with the surface. It is represented by |
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| where B is strength of magnetic field. A is area of the surface and q is the angle, which is normal, which the area makes with the direction of magnetic field. The S.I. unit of magnetic flux is weber which is the amount of magnetic flux over an area of 1m2 held normal to a uniform magnetic field of one tesla. |
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| Faraday discovered the phenomenon of Electromagnetic induction and established the following two laws of E.M.I. |
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| First law: Whenever the amount of magnetic flux linked with a circuit changes, an EMF is induced in the circuit. This induced EMF lasts so long as the change in magnetic flux continues. |
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| EMF induced in a circuit is directly proportional to the rate of change of magnetic flux linked with the circuit, i.e., |
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| The direction of induced EMF is given by Lenz's law. According to this law, the direction of induced EMF in a circuit always such as to oppose the change in magnetic flux responsible for it. |
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| Lenz's law is in accordance with the principle of conservation of energy. |
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| This is Fleming's right hand rule: According to this rule, if we stretch the first finger, the central finger and thumb of our right hand in mutually perpendicular directions, such that first finger points along the magnetic field and thumb points along the direction of motion of the conductor, then central finger would give us the direction of induced current. |
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| As is known, EMF is induced in a circuit only when amount of magnetic flux with the circuit changes. As f=BA cosq, therefore, three methods of producing induced EMF are |
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| (i) by changing B |
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| (ii) by changing A and |
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| (iii) by changing q. |
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| When a conductor of length l moves with a velocity V in a magnetic field of strength B so that magnetic flux linked with the circuit changes, the EMF induced (e) is given by |
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| e = B l v |
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| Eddy currents are the currents induced in the body of a conductor when the amount of magnetic flux linked with the conductor changes. These currents are also called Foucault currents. The magnitude of eddy current is given by |
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| where R is resistance of the conductor. The direction of eddy currents is given by Lenz's law or Flemming's right hand rule. |
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| Some of the important applications of eddy currents are: Electromagnetic damping, induction furnace, electromagnetic brakes, induction motor speedometers and in diathermy i.e., deep heat treatment of parts of human body. |
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| Some of the undesirable effects of eddy currents are that they oppose the relative motion, involve loss of energy in the form of heat and reduce the life of electrical devices. To minimize eddy currents, we use laminated cores. |
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| Self-induction is the property of an electrical circuit by virtue of which the circuit opposes any change in the strength of current flowing through it by inducing an EMF in itself. |
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| The value of L depends on geometry of the coil and is given by |
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| The S.I. unit of L is Henry. |
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| Mutual Induction is the property of two coils by virtue of which each opposes any change in the strength of current flowing through the other by developing an induced EMF. |
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| If f is the amount of magnetic flux linked with one coil when a current I flow through the other coil, then f = MI , where M is coefficient of mutual induction of two coils. |
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| Hence coefficient of mutual induction of two coils is equal to the EMF induced in one coil, when rate of change of current through the other coil is unity. The S.I. units of M is Henry. Coefficient of mutual inductance of two coils is said to be one Henry, when current changes at the rate of I ampere/sec. in one coil induces an EMF of one volt in the other coil. The value of M depends on geometry of two coils, distance between two coils, relative placement of two coils etc. |
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| The coefficient of mutual inductance of two long co-axial solenoids, each of length I, area of cross section A, wound on an air core is |
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| where N1, N2 are total number of turns of the two solenoids. |
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