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Laws of electromagnetic induction

Faraday's law states that the induced electromotive force (e.m.f.) is negatively proportional to the rate of change of magnetic flux.

This is expressed as: $$\mathcal{E}=-\frac{d\phi}{dt}$$

This means that the induced e.m.f. is negatively proportional to the gradient of the graph of magnetic flux vs time. Note that a negative e.m.f. implies an opposite direction of flow of current (i.e. reversed polarity).

The rate of change of magnetic flux hence depends on three factors: the change in magnetic flux density, the change in the area of the surface to be considered and the time taken for the flux to change.

The induced e.m.f. produces a current, which has an associated magnetic field. Lenz' law states that this magnetic field opposes the change in magnetic flux that induced the e.m.f.

This means that the current induced by a decrease in magnetic flux produces a magnetic field that increases the magnetic flux.

Fleming's right hand rule

The direction of the induced current in a straight conductor moving in a magnetic field can be determined using Fleming's right hand rule.

The rule involves extending the thumb, index and middle fingers of the right hand. These point in the direction motion of the conductor, the component of the magnetic field perpendicular to the motion of the conductor and induced current respectively.

The same abbreviation $FBI$ from the left hand rule can be used to recall what each finger represents, except that $F$ represents the direction of motion and not the force.

It is important to note that the right hand rule is used for generators (where induced currents are generated) and the left hand rule is used for motors (where forces are applied on charged particles and current carrying conductors).

Fleming's right hand rule for generators

Lenz's law

An induced e.m.f. produces a current with a magnetic field. Lenz' law states that this magnetic field opposes the change in magnetic flux that induced the e.m.f.

This means that the current induced by a decrease in magnetic flux produces a magnetic field that increases the magnetic flux.