Lenz's Law
The polarity of induced e.m.f in a closed circuit or coil is such that it oppose the cause which produces it.
Faraday 's law of electromagnetic induction, induced e.m.f. in a closed circuit is given by :
$E= -N \frac{d\Phi_B}{dt}$
Where:
* \mathcal{E} is the induced EMF
* N is the number of turns in the coil
* \frac{d\Phi_B}{dt} is the rate of change of magnetic flux through the coil
* Negative sign shows that induced e.m.f opposes the rate of change of magnetic flux in a closed circuit.
Conservation of Energy
Energy cannot be created or destroyed, but it can be transformed from one form to another within a closed system. The total amount of energy in an isolated system remains constant over time.
The Relationship Between Lenz's Law and Conservation of Energy :
Consider a bar magnet moving towards a coil of wire.As the magnet approaches, the magnetic flux through the coil increases.
According to Lenz's Law, the induced current in the coil will create a magnetic field that opposes this increase in flux. This means the coil will produce a magnetic pole facing the approaching magnet that is of the same polarity (e.g., North-North repulsion).
To continue moving the magnet towards the coil, you have to do work against this repulsive force.
This mechanical work done by you is converted into electrical energy in the coil, which can then be observed as an induced current and potentially heat.
Lenz's Law ensures that energy is conserved in electromagnetic induction by dictating the direction of the induced current in a way that requires an input of energy (work) to cause a change in magnetic flux and generate an induced current. The energy of the induced current comes from the work done against the opposing force.