  ## Electromagnetic Induction

- Are you feeling tough? Let make it extremely simple
1
Lenz's Law and Conservation of Energy:
According to this law, the polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it.  But whenever EMF is induced, it means electrical energy has been produced. But where did this energy come from? The mechanical energy spent by the external agent in moving the magnet relative to the coil changes the magnetic flux through that coil. The law of conservation must not be violated. So the induced current is such that it doesn't let the magnetic flux change through the coil.
• Its direction supports the decreasing magnetic flux.
• Its direction opposes the increasing magentic flux.

Let us see the consistency of Lenz's Law with Law of Conservation of Energy.
Lenz’s Law and Conservation of Energy
1 min
2
Relation Between Mutual and Self Inductance
Varying current in a coil can induce emf in a neighbouring coil. The magnitude of the induced EMF depends upon the rate of change of current and mutual inductance of the two coils.  Mutual inductance of a pair of coils, solenoids, etc., depends on their separation as well as their relative orientation. But can we find the mutual inductance for a pair of coils in terms of their self-inductance? Let's see the derivation for Relation Between Mutual and Self Inductance through this story.
3
Energy Consideration for motional emf:
Whenever a conducting rod of length l is moving with velocity v under uniform magnetic field B, a motional emf is induced in it. There will be a drift velocity of charges along the rod, so there will be a current in the road, and the consequent Lorentz force acting on them.
There will be a force on the arm. This force , is directed in the direction opposite to the velocity of the rod.  An agent must apply an equal and opposite force to move it with a constant velocity v. The agent must do work on the arm, i.e., spend mechanical energy.  This mechanical energy is dissipated as Joule Heat, given by

where I is the induced current due to motional emf (=Blv). This current causes heating and is dissipate due to the resistance of the conducting circuit.
This story will summarise the entire concept:
4  To calculate the emf, we can imagine a closed loop OPQ in which point O and P are connected with a resistor R and OQ is the rotating rod.  So now we can see that the area of the sector OPQ is changing with time because is also changing. Change in area will result in a change in the associated magnetic flux. Thus, we can obtain the expression of emf induced as the rate of change of magnetic flux.
Another approach can be to analyse this situation by considering Lorentz force. As the rod is rotated, free electrons in the rod move towards the outer end due to Lorentz force and get distributed over the ring. Thus, the resulting separation of charges produces an emf across the ends of the rod.
Here we have to consider an element of length dx at distance X from the centre which moves at right angles to the magnetic field. Motional EMF across it is given by:  We can integrate this result from x= 0 to x= l
The video will further polish our understanding of rotational EMF.
Class 12 Physics | #7 EMF Induced in a Rotating Conductor in Uniform Magnetic Field | For JEE & NEET
6 mins