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**Chapter 15. Electromagnetic Machines:**

__Magnetic Field and Field Lines__

- In A2/A-level physics, A magnetic field is a region in which a magnetic force will be exerted on any magneticmaterials in the area, these fields are represented by field lines. If field lines are drawnclose together then that represents a strong field, the closer the lines are together, then stronger the field.
- Wires carrying an electric current have amagnetic field around them

- A wire which has a current flowing through it, also has a magnetic field around it. If you curl you right hand, as shown thethe diagram, if you thumb is the direction of the electrical current, your curled fingers show the direction of the electrical field.

**A wire in a magnetic field**

- If a wire with a current moving through it is placed intoa magnetic field, the field incuded by the current in thewire distorts the original magnetic field, the original magnetic field, will oppose this change, creating aforce which can be calculated by the left hand rule.
- Thumb = Motion (Force)
- First finger = Magnetic Field
- Second finger = Current

__Calculating the magnitude of the force__

- At A Level you will only need to know about forces at right angles. This can be calculated using F=ILB.
- F is the force acting upon the wire.
- I is the current passing through the wire.
- L is the length of the wire inside the magnetic field.
- B is the magnetic field strength.
- (Note, its actually F = IL.B = |IL||B|sin(φ), however, since we only deal with φ=90º, this gives F=ILB).

**Magnetic Field Strength**

- Magnetic field strength, also know as flux density, is basically a measure of how strong thefield is. As we said earlier, the more field (or flux) lines there are within a certain area, thestronger the field. Magnetic flux is the total amount of magnetic flux around a magnet, theamount of the flux in a square meter, is called the flux density or magnetic field strength. Itis measures in Tesla (T) or Webers per square meter (Wb m-2). (Flux is measures in Webers (Wb)). This gives us: Flux = Flux Density × Area, Φ = BA.
- As a general rule, lines of flux, field lines, will try and become shorter and straighter, like anelastic string. This attracts North and South Poles together.

__Motors__

- We can use the face that a current in a magnetic wire causes a force to create an electricmotor.In the next diagram, we will introduce to new symbols. × and ●. × represents currentmoving into the page away from you and ● represents current coming out of the page towards you.
- With the situation on the right you have a field going from left toright, (first finger), and on the left a current going into the plan(second finger) and on the right it is coming out of the plane. Byusing the left-hand-rule you can see that there is a force on bothsides, moving the wire in an anti-clockwise direction.
- Of course once half a rotation has been made the currents will be the other way round sothe forces will be acting in the opposite direction. This can be stopped by a “split-ringcommutator”, this reverses the direction of the current every half turn so that it alwayscomes out of the plane on the left and into the plane on the right.

**Alternators**

- An alternator is basically the reverse of a motor, rather than a magnet and voltageproducing motion, motion and a magnet produce a voltage in exactly the same way. Adynamo or alternator is almost identical to a motor except it does not need the split ringand simply produces AC current.

__Flux Linkage__

- If you move a coil inside a magnetic field, an emf is induced inside the coil. The size of theemf is determined by the magnetic flux passing through the coil, (the number of flux lines itbreaks,) multiplied by the number of turns in the coil. This is known as flux linkage (ΦN).An emf is induced whenever flux lines are broken, however, this only results in a current ifthere is a complete circuit.

**Faraday's Law**

- “The induced emf is directly proportional to the rate of change of the flux linkage”.

- Hence, emf is the gradient of a graph of flux linkage against time and flux linkage is thearea under a graph of emf against time.

**Lenz's Law**

- “The induced emf is always in such as direction as to oppose the change that caused it”.This agrees with the conservation of energy, if the emf did no oppose the change butinstead enhanced it, you would get out far more energy than you put in.By combining Lenz's law with Faraday's law we get:

- You can use the left-hand-rule on this too.

**Transformers**

- Transformers use Lenz's and Faraday's law to change the voltage of an electrical currentwithout much power.
- A transformer is basically 2 coils wrapped round an iron core.
- An AC current in the primary or input coil produces a magnetic flux in the iron core.
- This magnetic flux then passes through the secondary oroutput coil, where it induces an alternating voltage, (of thesame frequency of the input voltage).

Since the number of coils is constant, using Faraday's law:

- As you can see from the final equations, more turns on the secondary coil, than on theprimary means that voltage will be increased, (Step Up). If there are less turns, it is a stepdown transformer and the voltage will be reduced.
- Transformers are used in the national grid, since the loss in energy due to resistance isproportional to current squared. by increasing voltage, you can decrease current and keepthe same power. Step down transformers are then used to provide the 230V for houses.

__Permeance and Magnetic Circuits__

- Because magnetic flux forms a closed loop, like an electrical circuit, you can use similarideas. Permeance is like conductance, but in a magnetic circuit instead. Like conductance,permeance can be increased by using a larger cross sectional area or a shorted length.
- Permeance = Permeability * (Cross sectional area / length).

- The permeance of a material is the amount of flux induced in it per current-turn.

__Energy loss in a transformer__

- In order for a transformer to be as efficient as possible, you want to maximize thepermeance in the core and maximize the conductance in the coild.

- To maximize the permeance, you want make L is small as possible, so make the iron coreshort, and you want to maximize A and μ. To maximize A you just need to make the corefat, and to maximize μ you need a material with high permeability, such as iron.

- To maximise the conductance you want to so the same. A thick wire and a cood conductorof electricity, such as copper. You also want to reduce the length, whilst keeping thecorrect number of coils, do this this you want a small a radius as possible, however, theradios has to go round the core which is as thick as possible. The best solution is simply acompromise of the two, so a fairly wide core, which the coil wrapped tightly around it.

- Unlike an electrical circuit, a magnetic circuit will still work if there is a gap in it, however,air has a very low permeability, so it should be avoided in transformers.

__Eddy currents__

- As well as loosing energy due to resistance and reluctance, some energy is also lost dueto eddy currents. A good magnetic conductor is iron, however, iron is also a good conductor of electricity.
- The alternating magnetic field, induces an emf across the iron core which due to the goodconductivity of iron, causes electrical currents flow.
- These currents then induce an flux themselves, which opposes the original changing fluxwhich created it. This reduces the overall flux in the iron core, meaning that less can beconverted back into electricity in the secondary coil. The loss in energy is released as heatby the currents in the iron core, which causes the core to become hot.
- One solution to minimize eddy currents is to make the core out of thin sheets of iron orlaminates, which are stuck together but separated by varnish which is permeable to fluxbut does not conduct electricity. This restricts the eddy currents to the laminations, causingthem to be significantly reduced.

**Three-phase generator**

- By putting 3 pairs of coils in 1 generator, you can get3 outputs, so effectively have 3 generators in 1. It'seven better than that though because, each of the 3outputs has a phase difference of 120º. When youcombine the 3 neutral outputs, they cancel eachother out, giving a current of approximately 0,meaning that only 1 thin wire is needed, rather than3 thicker ones.

__Rotating Field Motor__

- You can also create a motor based upon the same rotatingfield idea. By simply applying the 3 currents to a similar setup above, you can create a rotating magnetic field.Then simply placing a magnet inside that, which will followthe field will create a rotating motion.

And we're all done for today!

Drafted by Kin (Physics)