6.3.3 Electromagnetism

Electromagnetic induction occurs in the generators in power stations and in wind turbines. It generates electricity (induces an e.m.f) by relative motion between a conductor and a magnetic field. To induce an e.m.f all you need is a coil and a magnet. Attach a (sensitive) voltmeter to the coil. Push the magnet towards the oil, an e.m.f is induced across the ends of the coil (when the motion of the magnet is reversed a reverse e.m.f is induced. Repeating these motions will produce an alternating current. The faster the magnet moves the larger the induced e.m.f.

We can also use a simple d.c. electric motor in reverse (e.g using a falling mass to rotate the coil between the poles of the stationary magnet. The induced e.m.f can be large enough to operate a lamp. An e.m.f is induced in a loop of copper wire when it is moved perpendicular to the magnetic field lines of a magnet. The magnitude of the e.m.f is bigger when the wire is pulled away faster from the magnet.

As we all know, energy is ALWAYS conserved. Where does the electrical energy produced in the coil come from I hear you ask? Well, some of the work done to move the magnet is transferred into electrical energy. 

Magnetic flux
All experiments demonstrating electromagnetic induction can be explained in terms of magnetic flux (ϕ). The magnetic flux (ϕ) is defined as the product of the component of the magnetic flux density perpendicular to the area and the cross-sectional area:

ϕ = (Bcosθ) x A = BAcosθ

NOTE: When the field is normal to the area, cosθ = 1 and ϕ = BA.

The SI unit for magnetic flux is the weber (Wb). 1 Wb = 1 T m².

Magnetic flux linkage
This is the product of the number of turns in the coil N and the magnetic flux:

magnetic flux linkage = N ϕ

The SI unit of magnetic flux linkage is also Wb (sometimes weber-turns are used to distinguish it from magnetic flux).

It is important to realise that an e.m.f is induced in a circuit whenever there is a change in the magnetic flux linking the circuit. Since ϕ = BAcosθ you can induce an e.m.f by changing θ, B, or A.

Faraday's law
Faraday's law relates magnetic flux linkage to the magnitude of the e.m.f induced in conductors. It states that the magnitude of the induced e.m.f is directly proportional to the rate of change of magnetic flux linkage:

Ɛ ∝ Δ(Nϕ) / Δt

The constant of proportionality is -1:

Ɛ = -Δ(Nϕ) / Δt

Lenz's law
This states that the direction of the induced e.m.f or current is always such as to oppose the change producing it. The negative sign in the equation for Faraday's law is a mathematical way of expressing Lenz's law. In most calculations you can ignore this minus sign, it is just a reminder that energy cannot be created. 

We need to know how to investigate magnetic flux using search coils. The a.c. generator in the below diagram consists of a rectangular coil of cross-sectional area A and N turns of coil rotating in a uniform magnetic field of flux density B. The flux linkage for the coil is:

flux linkage = N ϕ =  = NBAcosθ

As the coil rotates (at a steady frequency) the flux linkage changes with time (t). The variation produced is sinusoidal and is caused by the changing cosθ:

We already know that Ɛ = -Δ(Nϕ) / Δt = Ɛ = -Δ(NBAcosθ) / Δt. This means that:

• The magnitude of the gradient of the magnetic flux linkage against time graph is equal to the induced e.m.f
• For a given generator, B, A, and N are all constant. This means that Ɛ ∝ -Δcosθ / Δ

The second graph shows the variation of e.m.f with time (t). The maximum induced e.m.f is directly proportional to:

• the magnetic flux density (B)
• the cross-sectional area (A) of the coil
• the number of turns (N)
• the frequency (f) of the rotating coil

Transformers

Okay hold your hats this i the last part of electromagnetism. An important use of electromagnetic induction is in transformers. These change alternating voltages to higher/lower values. A simple transformer consists of a laminated iron core, a primary/input coil, and a secondary/output coil. An a.c current is supplied to the primary coil which produces a varying magnetic flux in the soft iron core. The secondary coil (which is wound round the same core) is linked by this changing flux. The iron core ensures that all the magnetic flux created by the primary coil links to the secondary coil and none is lost. According to Faraday's law (the magnitude of the induced e.m.f is directly proportional to the rate of change of magnetic flux linkage) a varying e.m.f is produced across the ends of the secondary coil. The input and output voltages (Vp and Vs, respectively) are related to the number of turns on the primary and secondary coil (np and ns, respectively) by the turn-ratio equation:

ns/np = Vs/Vp (for an ideal transformer)

NOTE: A step up transformer has more turns on the secondary than primary coil. A step down transformer has fewer turns on the secondary that the primary coil.

So we need to know techniques and procedures used to investigate transformers:

• Set a multimeter to alternating voltage. This can be used to measure the input Vp and output Vs voltages
• This insulated copper wires are used to make primary and secondary coils
• Change the number of coils to see what happens to Vs for a fixed value of Vp and vice versa

For 100% efficient transformers the output power from the secondary soil is equal to the input power from the primary coil. P=IV so:

Vs Is = Vp Ip

This means that increasing input voltage by a factor of 100 will decrease output current by a factor of 100 etc.

We can make transformers more efficient by using low-resistance windings to reduce power losses due to the heating effect of the current. Making a laminated core with layers of iron separated by an insulator helps to minimise currents induced in the core itself (eddy currents) so minimalises loses due to heating. The core is also made of soft iron which is very easy to magnetise and demagnetise which improves the overall efficiency of the transformer.

Image credit: Kerboodle OCR A Physics textbook