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Devices like generators or batteries work in a way that the electric charge is transferred within the device, and in this process, energy is converted from one form to another. The terminals of these devices form opposite polarities. One terminal becomes negatively charged, whereas the other becomes positively charged. The energy gained in these devices or the work done on a unit electric charge is called electromotive force or emf. It is measured in volts. The process in which emf is induced in a circuit with the help of varying magnetic or electric fields is called electromagnetic induction.
Faraday’s law of electromagnetic induction
Michael Faraday introduced two laws known as Faraday’s law of electromagnetic induction.
Faraday’s first law
If the magnitude or the direction of the magnetic field is changed, emf will be induced in the wire, and this induced emf or induced voltage results in the induced current. Different ways in which this can be achieved are:
- By moving a magnet to and fro
- By changing the magnitude of the magnetic field
- By changing the orientation of the coil
- By moving the coil in and out of the magnetic field
Faraday’s second law
The rate of change of flux linked with the coil is equal to the value of emf induced in the coil. The flux induced is equal to the product of a number of turns in the coil and the flux associated with the coil.
E=NdΦ/dt … 1
Lenz’s law
Lenz’s law states that the direction of induced emf is such that it opposes the change that induced it. Let’s take an example of a bar magnet. If we move a bar magnet in and out of a coil, the emf would be induced. Moving the north pole of the magnet out of the coil would also induce the emf, and its direction would be in a way that opposes the change. In this case, moving out of the north pole induces emf. Therefore, the change would try to oppose it, i.e., the polarity at one end of the coil will become south to attract the north pole.
Now, using Lenz’s law in equation 1
E= -NdΦ/dt… 2
Emf induced in a moving conductor
Whenever a conductor is moved in a uniform magnetic field, emf is induced across the conductor. The emf is induced across the conductor because of the change in the area of the conductor that leaves and enters the magnetic field. In this way, magnetic flux is changed, which leads to the induction of emf. The induced emf is also known as motional emf. Now, let’s derive the expression for the magnitude of the emf induced.
According to Faraday’s law,
E=ΔΦ/Δt
Let’s consider a metallic rod of length l, moving at a speed of v. It will travel a distance of x,
in a time, t.
Velocity = distance/time
Or, v=Δx/Δt
As the area of the loop (induced emf) is constantly changing, the amount it gets changed by will be:
ΔA=lΔx
The magnetic flux is equal to the product of the magnetic field and the change in the area.
Therefore, 3 becomes
E=BΔA/Δt
=BlvΔt/Δt
=Blv
Therefore, emf induced across the conductor will be e=Blv.
The direction of induced emf, according to Lenz’s law, is in a way that opposes the change that’s producing it.
Problems
- Calculate the emf of a wire, moving with a velocity of 5 m/s through a uniform magnetic field of 0.5T. The length of the wire is 2 m.
The emf induced would be given by the following equation
E=Blv
= 0.5*2*5
= 5 volts
- A wire is 10 km long, moving at an orbital speed of 5 km/sec. Calculate the motional emf induced perpendicular to the Earth’s 5.00 × 10−5 T magnetic field.
E=Blv
=5*10-5*10*103*5*103
= 25*102=2500 volts
Conclusion
The magnetic field flux depends on the magnitude of the magnetic field, the orientation of the field, and the number of lines passing through a given surface area. If only a single factor varies, then emf would be induced, which in turn induces the current. Changing magnetic fields also produce eddy currents, which find their applications in magnetic levitation, welding, crack detection, etc. Electromagnetic induction has numerous applications, including devices such as generators, motors, and electrical components such as
