## Electrical machines – generators and motors

We have seen that when a conductor is moved in a magnetic field or when a magnet is moved near a conductor, a current flows in the conductor. The amount of current depends on:

- the speed at which the conductor experiences a changing magnetic field,
- the number of coils that make up the conductor, and
- the position of the plane of the conductor with respect to the magnetic field.

The effect of the orientation of the conductor with respect to the magnetic field is illustrated in the figure below.

If the emf induced and the current in the conductor were plotted as a function of the angle between the plane of the conductor and the magnetic field for a conductor that has a constant speed of rotation, then the induced emf and current would vary as shown in the figure below. The current alternates around zero and is known as an *alternating current* (abbreviated AC).

The angle changes as a function of time so the above plots can be mapped onto the time axis as well.

Recall Faraday’s Law, which you learnt about in a previous lesson:

### Definition: Faraday’s Law

The emf,\(\mathcal{E}\), induced around a single loop of conductor is proportional tothe rate of change of the magnetic flux, φ, through the area,\(A\), of the loop. This can be stated mathematically as:

\[\mathcal{E} =-N\frac{\Delta \phi }{\Delta t}\]

where \(\phi =B·A\cos\theta\) and \(B\) is the strength of the magnetic field.

Faraday’s Law relates induced emf to the rate of change of magnetic flux,which is the product of the magnetic field strength and the cross-sectionalarea the field lines pass through. The cross-sectional area changes as the loop of the conductor rotateswhich gives rise the \(\cos\theta\) factor. \(\theta\) is the angle betweenthe normal to the surface area of the loop of the conductor and the magnetic field.As the closed loop conductor changes orientation with respect to the magnetic field, the amount of magnetic flux through the area of the loop changes and an emf is induced in the conducting loop.