A-level Physics/Forces, Fields and Energy/Electromagnetic induction

We have already investigated that passing a current through a wire in a magnetic field causes a force to be exerted on it. The opposite is also true, and when a force is exerted on a wire a current is induced in the wire. This completely revolutionised the world because it meant that electricity could now be cheaper to produce.

Inducing an EMF.
When a conductor is moved through a magnetic field, an EMF is generated and the interaction of the magnetic field produced by the conductor with the magnetic field that was present cause deflection.

Faraday's Law
Michael Faraday state in his law that: The magnitude of the electromotive force(EMF) generated is proportional to the rate of change of magnetic field

Magnetic Flux density is a measure of the strength of a magnetic field and is essentially how dense the field lines of a magnetic field are within a given height.

Direction of induced current
Direction of induced current is according to the Lenz's law, which states that current in a coil is induced such that it always opposes the change producing it. For example, if we bring north pole of a magnet towards a neutral coil with some velocity, the current is induced in a way that it opposes the north pole or simply north pole is induced at the side where north pole is brought near which will result in the flow of current in the coil. If we assume a coil placed on a horizontal air space and bring north pole towards it from upper side and then we see coil from upper side, the current induced is in anti clockwise direction.

Calculating the induced EMF
Faraday's law states: Induced EMF is equal to the rate of change of magnetic flux. Magnetic flux = Magnetic field strength x Area = BA. Rate of change implies we consider the variable with respect to time (in seconds) Therefore...Induced EMF = (change in Magnetic Flux Density x Area)/change in Time. OR EMF = BA/t If we are doing it with a coil, the area becomes the area of one coil multiplied by the number of coils, A = πr2n Therefore, Induced EMF = (Bπr2n)/t. If we want to increase the amount of EMF induced, we either... Increase the area 'swept'. Increase the Magnetic Flux Density. Decrease the amount of time taken. The EMF induced is also proportional to the speed of the object going through the Magnetic Flux. Because BA/t can be re-written as...EMF = Magnetic flux density x Width x Speed. This is because speed = distance / time.

REMEMBER! - EMF is measured in volts, magnetic flux density is measured in teslas and area is measured in meters2, time is measured in seconds. So you will have to convert things from mm, cm, km, minutes, etc.

Faraday's law
The magnitude of induced EMF is proportional to the rate of change of magnetic flux linkage: $$E.M.F. \propto \frac{\Delta NBA}{\Delta t} \cdot\cos\left(x\right)$$

Lenz's law
Lenz's law states that the direction of the induced current is always so as to oppose the change which caused the current. It is just a small addition to Faraday's law:

$$E.M.F. = -\frac{\Delta NBA}{\Delta t}$$

(Notice the minus sign!)

Transformers
A transformer is made up of two or more coils of unmagnetised magnetic material. One coil is the primary coil and is connected to an alternating supply. The other is the secondary coil.

When an alternating current is set up in the primary coil, it produces a changing magnetic flux, this changing magnetic flux causes an induced electromotive force (e.m.f) in the secondary coil.

Transformers can be used to increase or decrease the voltage by changing the number of turns in the primary and secondary coils.