Electromagnetic Induction
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| Discuss Electromagnetic Induction ELECTROMAGNETIC INDUCTION
What is electromagnetic induction?
It is defined as a process in which, production of an electromotive force takes place in a conductor when there is a change of magnetic flux linked with the conductor or when there is a relative motion of the conductor across a varying magnetic field.
FARADAY’S LAW OF ELECTROMAGNETIC INDUCTION
‘When the magnetic flux through a circuit is changes. An induced emf is set up in the circuit ‘
We can also say that whenever the magnetic flux through an area bounded by closed conducting loop changes, an emf is produced in thy loop. the magnitude of this emf is given by
|
E = -dF/dt |
Where dF is the change in flux of the magnetic field in time t. If dF is in weber and dt in seconds, then the unit of E is given by Volts.
NOTE: if the circuit is an open circuit, an emf will be induced, but there will be no current in the circuit. Thus, we can say that the change in flux induces emf but not a current.
LENZ’S LAW
‘The direction of the induced current is such that it opposes the change that has induced it.’
Thus, we can say that the direction of the induced emf or current is such that it opposes the change that has produced it. If the direction of the induced current were not in accordance with Lenz’s law, then we would be obtaining electrical energy continuously without doing any work, which is not possible. Thus, we see that Lenz’s law is just a modification of principle of conservation of energy.
MOTIONAL EMF
When a conductor of length l moves in a magnetic field B with a velocity v, as shown in the figure, at this stage the electrons in the rod experience a force. This force pushes them at the lower end of the rod. The force on an electron is given by Fm = -qvBsinq. Due to this movement of electrons in the rod, a charge separation takes place and this gives rise to a potential difference and an electric field along the length of the rod. This induced electric field is directed along the lower end. The electric force on the electrons of total charge q is given by
|
Fe = -qE |
Therefore, the net force on the electrons is given by
F = Fe + Fm
F = -q (E + vXb)
In the steady state of electrons, when the electric force balances the magnetic force on the electrons, the net force becomes 0. Thus, in the steady state we have,
0 = -q(E + vBsinq )
Therefore, E = v X B
And the potential difference between the lower and upper ends is given by
V = (v X B). l
NOTE: the length of the rod behaves like an internal circuit of a battery. For the external circuit, the upper end is positive and the lower end is negative.
If the resistance of the rod is r and the resistance of the external circuit is R, then the current in the circuit is given as
I = [VBl]/(r + R)
SELF INDUCTION
The phenomenon of production of an induced emf in the circuit due to the change in its own current is called self-induction. At any moment, the magnetic flux associated with the circuit is proportional to the perpendicular magnetic field associated with it. Since this magnetic field depends upon the electric current flowing in the circuit, so the magnetic flux linked with the circuit is proportional to the electric current flowing in the circuit.
The total flux linked with all N turns of the circuit (coil) is given as NF = Li. Where L is a proportionality constant. For a given current, this constant decides the flux linked with the circuit, so it may be called a measure of self-inductance or the self-induction coefficient.
When i = 1A then L = NF. So the self induction of a circuit is equal to that flux which is associated with it when the current flowing in the circuit is 1A. This may also be defined as the induced emf associated with the circuit when the rate of change of current in the circuit is one ampere per second.
NF = Li
NdF/dt = Ldi/dt
-Ein = Ldi/dt
| L = Ein/(di/dt) |
The phenomenon of production of induced emf in the coil due to a change in current in another coil is called mutual induction. The first coil may be called the primary coil and the second coil may be called the secondary coil.
When two coils are placed close to each other, such that the current in one coil changes with time, then the magnetic flux linked with the secondary coil is proportional to the current in the primary coil. So, if the Current in the primary coil is ip and the emf induced in the secondary coil is Fs and the number of turns in the secondary coil be Ns.
NsFs is proportional to ip
NsFs = Mip
Or M = NsFs /ip
Where M is the mutual induction coefficient and is defined as the flux linked with the secondary coil when the current in the primary coil is 1A.
Now
NsFs = Mip
Or Ns(dFs /dt) = M(dip/dt)
Es in = M(dip/dt)
M = Es in / (dip/dt)
If dip/dt = 1 amp/sec
Then M = Es in
So the mutual induction coefficient between two coils is that induced emf which appears or is produced in the secondary coil, when the rate of change of current in the primary coil is 1amp/sec.
