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Faraday’s law implies that the induced emf is equal to the negative time rate of change of the magnetic flux. The magnetic flux is proportional to the magnetic field due to the source current, which in turn is proportional to the source current in the circuit. Thus, a self induced emf (єL) is always proportional to the time rate of change of the source current. For a closely spaced coil of N turns carrying a current of I, the self induced emf is given as:
where L is a proportionality constant called the inductance of the coil, which depends upon the geometry of the circuit and other physical characteristics. Now the inductance of a coil containing N turns is given as:
Thus, the inductance is a measure of the opposition to a change in current. And the inductance of a device depends upon its geometry.
The mutual inductance can be measured by considering the magnetic flux linked with the area enclosed by a circuit. If this magnetic flux varies with time due to time varying currents in nearby circuits, then there is an induction of emf in the second circuit due to the first. Consider two closely wound coils of wire as shown in the figure below.
The mutual inductance of coil 2 with respect to coil 1 (M12) is given by,
The corresponding emfs induced with each coil due to the other are given as follows:
Thus, in mutual induction the emf induced in one coil is always proportional to the rate at which the current in the other coil is changing. It can be shown that M12=M21=M. The unit of mutual inductance is henry
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Electromagnetism