Rate of change of Magnetic flux is the core concept of Electromagnetic Induction. The induced EMF is directly proportional to this quantity.
This article discusses the concept in a bit more detail.Introduction to rate of change of magnetic fluxThe phenomenon of developing induced emf by changing the magnetic flux is called the electromagnetic induction.
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The phenomenon was introduced by the U.K. scientist Michael Faraday. Michael Faraday gives the laws of electromagnetic induction, which are based on the rate of change of magnetic flux.Faraday’s laws for the rate of change of magnetic fluxFaraday’s gave the two law of electromagnetic induction. Out of which, the second law is properly based on the rate of change of magnetic flux.
Faraday’s second law of electromagnetic induction states that, the magnitude of induced emf in a circuit directly varies to the rate of change of magnetic flux linked with the circuit. Consider a coil placed in the space and a magnet moved faster either magnet is approaching the coil or receding the coil, the magnetic flux linked with coil with the faster rate. Therefore, the galvanometer, which is attached to the coil, shows more deflection and hence the induced emf is more. If the magnet moved slowly, the deflection in the galvanometer is small, which indicates that the induced emf is small.
Thus, we can say that the induced emf developed in the coil directly varies to the rate of change of magnetic flux.Let `phi1` be the amount of magnetic flux linked with the coil at any time and `phi2` be the amount of magnetic flux linked with coil after t seconds, thenRate of change of magnetic flux = (`phi`2 - `phi`1) / tAccording to the Faraday’s second law of electromagnetic induction, we get induced emf directly varies to the rate of change of magnetic flux linkede `prop` (`phi`2 - `phi`1) / tor, e = k (`phi`2 - `phi`1) / twhere, k is the constant of proportionality and experimentally the value of k is 1.So , e = (`phi`2 - `phi`1) / tIf d`phi` is the small change in the magnetic flux in small time dt, we can write ase = - d`phi` / dtNegative sign is taken because induced emf always opposes the change magnetic flux linked with the coil.Example for the rate of change of magnetic flux
he magnetic flux linked with a coil changes from 0.012 Weber to 0.005 Weber in 0.01 seconds. What is the magnitude of induced emf in the coil.Solution`phi`1 = 0.012 Weber, `phi`2 = 0.005 Weber, dt = 0.01 seconde = (`phi`2 - `phi`1) / t = (0.005 – 0.012) / 0.01 = 0.7 Volt