SPH3U Magnetic Fields, Motors and Transformers: Notes and Practice

Electricity and magnetism are not two subjects but one. A current creates a magnetic field; a changing magnetic field creates a current. Those two sentences are the basis of every motor, generator and transformer ever built.

Magnetic fields

Fig 1Field lines run out of the north pole and into the south, and never cross.

Every magnet has a north and a south pole. Cut one in half and you get two smaller magnets, never an isolated pole.
Like poles repel, opposite poles attract — the same pattern as electric charge.
Field lines run from north to south outside the magnet, and never cross one another.
Where the lines are closer together, the field is stronger.
Only a few materials are ferromagnetic — iron, nickel, cobalt and their alloys.

Earth's magnetic field is backwards

A compass needle's north-seeking pole points toward geographic north, and opposite poles attract — so what sits near the geographic north pole is magnetically a south pole. The field also protects the planet, deflecting charged particles from the Sun and producing the aurora where they funnel in near the poles.

Current makes a magnetic field

Fig 2Two rules, one for a straight wire and one for a coil. Both use conventional current.

Rule	Thumb points	Fingers show
Straight conductor	Along the conventional current	Curl in the direction of the circular field
Coil or solenoid	Out of the north pole of the coil	Curl in the direction of the current in the windings

Right hand, conventional current

These rules are stated for conventional current — positive to negative — using the right hand. Some older resources use a left-hand rule with electron flow instead. Both give the same physical answer, but mixing them gives the opposite one, so state which convention you are using every time.

Electromagnets

Fig 3A coil concentrates the field; an iron core multiplies it.

F_{M} \propto I F_{M} \propto n F_{M} \propto κ

Strength is proportional to current, to the number of turns, and to the core material factor.

An electromagnet is a coil of wire, usually wound on an iron core. Three things make it stronger: more current $I$ , more turns $n$ , and a better core material — the factor $κ$ , which for soft iron can be in the hundreds. These are proportional relationships only; this course does not calculate field strengths numerically.

The advantage over a permanent magnet

An electromagnet can be switched off, and its strength can be varied by changing the current. That is why scrapyard cranes, maglev trains, MRI scanners, relays and doorbells all use electromagnets — a permanent magnet cannot release its load on command.

The motor principle

Fig 4A current-carrying wire in a magnetic field experiences a force at right angles to both.

Place a current-carrying wire in a magnetic field and it experiences a force, perpendicular to both the current and the field. Mount a loop of wire on an axle in a field and the forces on the two sides act in opposite directions, so the loop rotates. That is a motor.

A split-ring commutator reverses the current every half turn, so the loop keeps rotating the same way instead of stopping at the halfway point.
A generator is the same machine run backwards: turn the loop mechanically and a current appears. This is electromagnetic induction.
Induction needs change: a stationary magnet in a stationary coil induces nothing. It is the motion, or the changing current, that produces the voltage.
Every power station — nuclear, hydro, gas, wind — is a way of spinning a generator. Only the method of spinning differs.

Transformers

Fig 5Two coils on one iron core. The turns ratio sets everything.

A transformer is two coils wound on a shared iron core. Alternating current in the primary creates a continuously changing magnetic field, which induces a voltage in the secondary. The ratio of turns decides how the voltage changes.

\frac{N _{1}}{N _{2}} = \frac{V _{1}}{V _{2}} = \frac{I _{2}}{I _{1}}

Note that the current ratio is inverted — more turns means more volts but less current.

The current ratio is upside down

\frac{N _{1}}{N _{2}} = \frac{V _{1}}{V _{2}}

, but it equals

\frac{I _{2}}{I _{1}}

— with the subscripts reversed. This follows from energy conservation: an ideal transformer cannot create power, so if the voltage goes up the current must come down by the same factor. Getting this backwards is the standard error.

AStep-up transformer

More turns on the secondary ( $N_{2} > N_{1}$ )
Voltage increases
Current decreases by the same factor
Used leaving a power station

BStep-down transformer

Fewer turns on the secondary ( $N_{2} < N_{1}$ )
Voltage decreases
Current increases by the same factor
Used on the pole outside a house

Transformers only work on AC

Induction requires a changing magnetic field. A steady direct current produces a steady field, which induces nothing in the secondary. This is the decisive reason the grid distributes alternating current — without AC, long-distance transmission at high voltage would be impossible.

Why the grid uses very high voltage

Fig 6Step up for the journey, step down for the customer.

Power lost as heat in a transmission line is $P_{l oss} = I^{2} R$ . The line's resistance is fixed by its material and length, so the only way to cut losses is to reduce the current. Since $P = V I$ , delivering the same power at a higher voltage requires proportionally less current — and because the loss depends on $I^{2}$ , cutting the current by ten cuts the losses by a hundred.

Stage	Typical voltage	What happens
Generator at the station	$20 kV$	Electricity is produced
Step-up transformer	$230$ – $500 kV$	Voltage raised for transmission
Transmission lines	$230$ – $500 kV$	Low current keeps $I^{2} R$ losses small
Substation	$27.6 kV$	Stepped down for local distribution
Pole transformer	$120/240 V$	Stepped down again for the house

Magnetic Fields, Motors and Transformers

Key things to remember

Magnetic fields

Current makes a magnetic field

Electromagnets

The motor principle

Transformers

Why the grid uses very high voltage

Worked examples

Where marks get lost

Flashcards 12

Practice