Electricity and Magnetism Together - Physics for Pilot Assessments

Electricity and magnetism are not two subjects but two aspects of one, and the link runs both ways: a current produces a magnetic field, and a changing magnetic field produces a voltage. Between them those two statements account for every motor, every generator, every transformer and every relay. By the end of this lesson you should be able to describe the field around a current-carrying wire and around a coil, work out the force on a current in a field and run that calculation backwards, say precisely what has to happen for a voltage to be induced, use a transformer's turns ratio in both directions, and explain in a sentence what a relay and a dynamo each do.

A current makes a field

Send a current down a straight wire and a magnetic field appears around it — not along the wire but circling it, in closed loops centred on the wire and lying in planes at right angles to it. Hold a compass near a wire carrying a substantial current and the needle swings; reverse the current and it swings the other way. The strength of the field falls off as you move away from the wire, and it grows in proportion to the current, so the two ways to get a stronger field from a straight wire are to increase the current or to get closer.

The direction is given by the right-hand grip rule, which is worth doing physically once rather than reading twice: point the thumb of your right hand along the direction of the conventional current, curl your fingers, and your fingers point the way round the field goes. Looking at the wire end-on with the current coming towards you, the field circles anticlockwise.

A single straight wire produces a weak field, and the standard way to make it useful is to wind the wire into a coil, called a solenoid. Each turn contributes its own field, and inside the coil all of those contributions point the same way and add up, giving a strong, nearly uniform field along the coil's axis and a field outside that looks remarkably like the bar magnet's from the previous lesson — one end behaves as a north pole and the other as a south, and reversing the current swaps them over. Three things make such an electromagnet stronger: more current, more turns of wire, and an iron core inside the coil. The iron works because it is a soft magnetic material, so it magnetises along with the applied field and adds its own contribution, and then loses that magnetism again when the current stops — which is the whole point of an electromagnet as against a permanent one. You can switch it off.

The motor effect

Now put a current-carrying wire into someone else's magnetic field. The wire has its own field circling it, the magnet has its field crossing the region, and the two do not simply coexist: the wire experiences a force. That force is at right angles both to the field and to the current, which is the part that no amount of prose makes obvious and the figure exists to carry. Reverse either the current or the field and the force reverses; reverse both and it goes back to its original direction. If the wire lies along the field rather than across it there is no force at all, and at angles in between the force is somewhere between the two extremes.

On the left, the wire seen end-on with the current coming towards you: the field forms closed circles around it, anticlockwise by the right-hand grip rule, and weakens further out. On the right, that same wire placed in a field running from the north pole to the south pole — the force on it is at right angles to both the field and the current, which is what makes a motor turn.

The size of the force depends on three things, each in direct proportion: the strength of the field, the current in the wire, and the length of wire that is actually inside the field. Field strength gets its own unit here, the tesla, written T, and a tesla is a large field — the field between the poles of a strong laboratory magnet is around one tesla, while the Earth's is a few hundred-thousandths of one.

Force on a current in a magnetic field

F = B I L

$F$: the force on the wire, in newtons (N)
$B$: the magnetic field strength, in tesla (T)
$I$: the current in the wire, in amperes (A)
$L$: the length of wire inside the field, in metres (m)

That relationship assumes the wire is at right angles to the field, which is how these questions are always set and how a motor is always built. A motor is nothing more than this effect arranged to keep going: a coil sits in a field, the current in one side of the coil runs opposite to the current in the other side, so the forces on the two sides push in opposite directions and the coil turns. Left alone it would stop after half a turn, when the forces would start opposing the rotation, so the connections are reversed at that moment by a switching contact called a commutator, and the push continues in the same rotational direction.

Example 1 — the force, and then the current

A wire carrying 4 A lies at right angles to a field of 0.5 T, with 0.2 m of its length inside the field. What force acts on it? And what current would be needed to double that force with the same field and length?

Force = field × current × length = 0.5 × 4 × 0.2.
Take it in two steps: 0.5 × 4 = 2, and 2 × 0.2 = 0.4 newtons.
For the second part, the force is proportional to the current at fixed field and length, so doubling the force needs double the current: 8 A.
Check it: $F = 0.5 \times 8 \times 0.2 = 0.8\ \text{N}$ That is twice 0.4 N.
Note what would not have worked: doubling the length of wire in the field also doubles the force, and so does doubling the field, because all three factors enter in direct proportion. Only the direction depends on which of them you reverse.

Induction: the effect run backwards

The link works in the other direction too, and this is the more surprising half. Move a magnet near a coil of wire and a voltage appears across the ends of the coil; if the coil is part of a complete circuit, a current flows. Nothing is connected to anything, and no supply is involved — the voltage is generated, or induced, by the movement itself. Move the magnet the other way and the induced voltage reverses. Move it faster and the voltage is larger. Use more turns on the coil, or a stronger magnet, and it is larger again.

The word to hold on to is change. What induces a voltage is a change in the magnetic field passing through the coil, and if nothing is changing there is no voltage, however strong the field. A magnet held stationary next to a coil, however powerful and however close, induces exactly nothing; the instant it starts to move, a voltage appears; the instant it stops, the voltage disappears again. It does not matter which of the two is moved — moving the coil past a stationary magnet works just as well, because what matters is the relative change. And a field that changes without anything moving at all works too, which is what makes the transformer below possible.

Example 2 — what induces a voltage, and what does not

A coil of wire is connected to a sensitive voltmeter. Decide what the meter shows in each case. (a) A powerful magnet is held completely still inside the coil. (b) The same magnet is pulled slowly out of the coil. (c) It is pulled out quickly instead. (d) The magnet is held still and the coil is moved away from it. (e) The coil is rewound with twice as many turns and the quick pull is repeated.

(a) Nothing at all. However strong the field, it is not changing, and only change induces a voltage — the strength of a stationary field is irrelevant.
(b) A small voltage appears, and only while the magnet is actually moving: the field through the coil is falling, and that change is what the coil responds to.
(c) A larger voltage than in (b). The same total change happens in less time, and a faster change induces more.
(d) Exactly the same as pulling the magnet out. What matters is the relative movement between the two, so it makes no difference which of them does the moving.
(e) About twice the voltage of (c): every turn has the same changing field through it, and each turn's contribution adds to the total.
In every case the reading returns to zero the instant the movement stops. A voltage is induced only while the change is happening — which is the single sentence most of the questions on this topic are testing.

The dynamo and the generator

Induction becomes useful when the change is made to repeat. Mount a coil between the poles of a magnet and turn it: as the coil rotates, the amount of field passing through it changes continuously, so a voltage is induced continuously, and the faster you turn it the larger that voltage is. That is a generator, and the small version fitted to a bicycle wheel is a dynamo. The coil's ends are brought out to the external circuit through sliding contacts — rings that the coil turns with, pressed against fixed brushes — because a coil that is rotating cannot be wired directly to something that is not.

Left, a relay: a small current in the control circuit makes the coil a magnet, which pulls the contacts of the load circuit shut — so a switch carrying a fraction of an amp controls a circuit carrying many amps, and the two circuits share no wire. Right, a dynamo: turning the coil in the field changes the field through it, which induces a voltage, taken out to the lamp through the slip rings.

There is a satisfying symmetry to notice, because a motor and a generator are the same machine used two ways. Put a current into a coil in a field and it turns, which is the motor effect. Turn a coil in a field and a current comes out, which is induction. Nothing has been added to the hardware between the two descriptions. It is also worth being clear that a generator does not create energy: whatever electrical energy comes out has to be put in mechanically, which is why a bicycle dynamo makes the pedals harder to push the moment its lamp is switched on, and why generating more electricity means burning more fuel.

AC and DC

A rotating coil produces a voltage that rises, falls, reverses and rises again, once per revolution, because the coil's relationship to the field reverses twice per turn. A supply of that kind is called alternating current, or AC, and one that flows steadily in a single direction, as a cell provides, is direct current, or DC. The number of complete cycles per second is the frequency, measured in hertz as in the waves module: European mains is 50 Hz, meaning fifty complete reversals-and-back every second, and North American mains is 60 Hz. Nothing about AC makes it weaker or less useful — a 230 V AC supply lights a lamp exactly as a 230 V DC supply would — but one thing does depend on it absolutely, and that is the transformer.

The transformer

Wind two separate coils onto the same iron core, so that they share no electrical connection at all, and put an alternating current through the first one. That current makes a magnetic field in the core; because the current is alternating, the field is constantly changing; and a changing field through the second coil induces a voltage in it. Energy has crossed from one circuit to the other with no wire between them. Now the useful part: how big the induced voltage is depends on how many turns each coil has, because each turn of the second coil has the same changing field passing through it and contributes its own share.

Transformer turns ratio

\frac{V_s}{V_p} = \frac{N_s}{N_p}

$V_p$: the voltage across the primary — the input coil — in volts (V)
$V_s$: the voltage across the secondary — the output coil — in volts (V)
$N_p$: the number of turns of wire on the primary coil
$N_s$: the number of turns of wire on the secondary coil

Read it as a proportion and it is easy to use: the voltages are in the same ratio as the turns. Twice as many turns on the secondary as on the primary gives twice the voltage out, which is a step-up transformer; half as many gives half the voltage, a step-down transformer. Rearranging it by multiplying both sides by the primary voltage gives the output directly: the secondary voltage equals the primary voltage multiplied by the turns ratio.

What a transformer cannot do is increase the power, and that limit is the one items test. Energy is conserved, so ignoring the small losses in a real transformer, the power taken from the secondary cannot exceed the power supplied to the primary — and since power is voltage multiplied by current, a transformer that doubles the voltage must halve the available current. There is no free energy in the ratio; there is a trade, exactly as there was in the hydraulic press of the fluids module.

Power in equals power out, for an ideal transformer

V_p I_p = V_s I_s

$V_p, I_p$: the primary voltage in volts (V) and primary current in amperes (A)
$V_s, I_s$: the secondary voltage in volts (V) and secondary current in amperes (A)

And this is where AC becomes indispensable rather than merely conventional. A transformer works only because the field in the core is changing, and a steady direct current makes a steady field, which induces nothing at all. Connect a transformer to a battery and you get a single brief pulse in the secondary as the current is switched on, another as it is switched off, and nothing whatsoever in between. That, rather than any historical accident, is why mains electricity is distributed as AC: transformers can raise it to a very high voltage for transmission, which for a given power delivered means a much smaller current, and a smaller current means far less power wasted heating the cables — the current squared multiplied by the resistance, from the power lesson.

Example 3 — a turns ratio, both ways

A transformer has 100 turns on its primary and 200 on its secondary, with 230 V AC applied to the primary. What is the secondary voltage? If the primary draws 2 A, what current is available from the secondary? And how many secondary turns would be needed to get 23 V from the same 230 V primary?

The turns ratio is $\frac{\text{secondary}}{\text{primary}} = \frac{200}{100} = 2$ , so the secondary has twice as many turns.
The voltages are in the same ratio, so the secondary voltage is 230 × 2 = 460 volts. This is a step-up transformer.
For the current, use power in = power out: the primary power is 230 × 2 = 460 watts, so the secondary can supply 460 W at 460 V, which is a current of $\frac{460}{460} = 1$ ampere.
Double the voltage, half the current — the power is the same 460 W on both sides, and nothing has been gained.
For the last part, 23 V is a tenth of 230 V, so the secondary needs a tenth of the turns: $N_s = \frac{100}{10} = 10\ \text{turns}$
Check it as a ratio: $\frac{10}{100} = 0.1$ , and 230 × 0.1 = 23 volts.

The relay

The last device is the simplest and the most widely used, and it exists because an electromagnet can be switched off. A relay is two separate circuits with no electrical connection between them: a control circuit containing a small switch and a coil, and a load circuit containing whatever actually needs the power. Send a small current through the coil and it becomes a magnet, which attracts a pivoted iron arm; the arm carries a contact, and moving it pushes the contacts of the load circuit together and completes it. Switch the small current off, the coil stops being a magnet, a spring pulls the arm back, and the load circuit opens again.

What that buys you is worth stating plainly, because it is what questions ask. A tiny current in a light, cheap switch controls a very large current in a heavy cable, so the switch you actually touch never has to carry the load — which is why a car's starter motor, drawing hundreds of amps, is operated by a key that carries a fraction of an amp. It also isolates the two circuits from each other, so the control side can run at a low, safe voltage while the load side runs at a dangerous one, and it lets a control circuit somewhere convenient operate a load circuit somewhere inconvenient. The practical drilling on relay behaviour belongs to the electrical exercises; what matters here is that a relay is an electromagnet used as a switch.

Why it matters in aviation

Both halves of this lesson are at work whenever an aircraft's systems move. A current in a magnetic field produces a force, and that force drives the electric motors behind flap and trim actuation, fuel pumps and cooling fans, and it pulls the armature in the solenoids and relays that let a small switch on the flight deck close a circuit carrying a very large current elsewhere. Run the same physics backwards and it produces the power in the first place: engine-driven machines turn coils in a magnetic field, and the changing field through those coils induces the voltage that feeds the busbars.

Because a rotating machine naturally gives alternating current, and because a transformer works only on a changing field, part of an aircraft's distribution is alternating so that voltages can be changed where each system needs a different one. Transport aircraft typically distribute 115 V AC at 400 Hz rather than at the 50 or 60 Hz of a domestic supply, and the reason belongs to this lesson: at a higher frequency the transformers and motors doing these jobs can be made smaller and lighter.

What the test asks

The dominant distractor across this whole lesson is a stationary magnet inducing a voltage — an item describing a strong magnet held close to a coil and offering a large induced EMF among the options. Nothing is induced unless something changes, so the word to hunt for in the stem is a verb of motion or a mention of alternating current. Its companion is the transformer on a battery, which does nothing continuous for the same reason. Expect a motor-effect item in which the force is offered as being along the field or along the current, when it is at right angles to both. Expect an electromagnet item where the wrong answer strengthens it by using a steel core instead of iron, or by reversing the current, which changes only the direction. And expect a transformer item offering more voltage and the same current at the output, which would be more power out than in.