Analyse qualitatively and quantitatively, with reference to energy transfers and transformations, examples of Faraday’s Law and Lenz’s Law

Electromagnetism > Electromagnetic Induction >

Faraday noted that when the flux passing through an area changed, it created an electromotive force

He noted:

Moving a magnet through a coil gives a current.
Produced in a direction opposite to movement.
Speed of movement affects current magnitude and magnet direction affects current direction.

Faraday’s Law : when the magnetic flux linking a circuit changes, an electromotive force is induced in the circuit proportional to the rate of change of the flux linkage

Independently Lenz also noted this effect. In addition he also noted the direction of current in relation to change in flux.

He noted:

that induced current opposes the changing magnetic field that created it.
Relative motion of a coil and magnetic field produces a current which cannot build in the same direction as it violates the conservation of energy
The current going backwards (back EMF) conserves energy.
Opposes motion of motors (otherwise this would produce free energy)

Lenz’s Law : the current induced in a circuit due to a change or a motion in a magnetic field is so directed as to oppose the change in flux and to exert a mechanical force opposing the motion.

Induced E.M.F. due to change in flux is thus given by :

, where is the flux passing through the are of the coil.

Examples :

EMF produced by the relative movement between a magnet and straight conductors

If a straight conductor is moving perpendicularly through a magnetic field, then the charged particles in the conductor will experience a force equivalent to : F_b = qvB.
The free charged particles will move such that an opposing electric field E is developed within the straight conductor . This electric field will produce force : F_E = qE
The charge separation continues until the two forces create equilibrium.
Then the electric field in equilibrium is E = vB
The potential difference due to this electric field is
Thus the kinetic energy of the moving conductor has been converted to EMF.

EMF produced by the relative movement between a magnet and metal plates

These are also called eddy currents.
If the magnetic field through a metal plate is changed such that flux through the plate changes, then a current is set up in the metal plate.
This induced current sets up a magnetic field which opposes the change in magnetic field through the plate.

Eddy currents create a force that opposes the movement of the plate that is responsible for the change in magnetic field through the plate.

EMF produced by the relative movement between a magnet and solenoids

If we change the flux passing through a coil by moving a bar magnet as shown in the picture below, a current is induced.

The induced current creates a magnetic field that opposes the motion of the magnet.
Thus force needs to be applied to move the magnet, and work gets done in this movement.
This work that is done gets converted to the EMF that associated with the induced current.
Thus total energy is conserved.
If there are multiple coils creating a solenoid , then each coil adds to the EMF produced.

Then EMF produced is : , N is the number of coils

The generation of an emf produced by the relative movement or changes in current in one solenoid in the vicinity of another solenoid

The current I₁ in Solenoid A creates a magnetic field which passes through the Solenoid B
If the Solenoid A or B is moved , then the flux passing through Solenoid B changes .
- This gives rise to EMF and inductance current in solenoid B.
If the current I₁ is changed, the magnetic field strength due to the current changes and flux passing through the solenoid B changes.
- This gives rise to EMF and inductance current in solenoid B.
This is called Mutual Inductance.