Electromagnetism and the Motor Effect

When a current flows through a wire, it produces a magnetic field in the space around the wire. This is the link between electricity and magnetism, and it is the foundation of every electromagnetic device.

For a straight wire, the field lines form concentric circles around the wire, lying in a plane at right angles to it. Two factors set the strength of the field:

• the size of the current — a larger current gives a stronger field;
• the distance from the wire — the field gets weaker as you move away.

Reversing the direction of the current reverses the direction of the magnetic field around the wire.

You can demonstrate this effect by threading a wire vertically through a piece of card and sprinkling iron filings on the card. When the current is switched on, the filings settle into circular rings, revealing the field. Small plotting compasses placed on the card line up along these circles and flip round when the current reverses.

A single straight wire makes only a weak field. Winding the wire into a coil, called a solenoid, adds the fields of every turn together and concentrates them.

Inside a solenoid the field is:

• strong, because the turns reinforce one another;
• uniform, meaning the field lines are parallel, evenly spaced and point the same way.

The magnetic field outside a solenoid has the same shape as the field around a bar magnet, with a north pole at one end and a south pole at the other.

This is why a solenoid is so useful: it behaves like a bar magnet, but one you can control with a switch. Adding more turns to the coil or increasing the current makes the field inside stronger.

Field region	Shape and strength
Inside solenoid	Strong and uniform (parallel, even field lines)
Outside solenoid	Like a bar magnet, with a north and south pole

An electromagnet is a solenoid with a core of soft iron placed inside it. Iron is magnetic and easily magnetised, so it becomes strongly magnetic when the current flows, greatly increasing the field of the coil.

The key advantage is control. Because the iron loses its magnetism when the current stops, the electromagnet can be switched on and off, and its strength varied, simply by controlling the current.

You can strengthen an electromagnet in three ways:

• increase the current through the coil;
• add more turns to the coil;
• use an iron core (rather than an air core).

(Separate Physics only) You may be asked to interpret a diagram of an electromagnetic device — such as an electric bell, a relay or a scrapyard crane — and explain how it works using these ideas.

For example, an electric bell uses an electromagnet that repeatedly attracts an iron armature; each time the armature moves it breaks the circuit, the electromagnet switches off, a spring pulls the armature back, the circuit remakes, and the cycle repeats to ring the bell.

(Higher Tier only) The whole of this slide and the next is Higher Tier content.

When a current-carrying conductor is placed in a magnetic field, the field of the magnet and the field of the current interact, and the wire experiences a force. This is the motor effect. By Newton's third law, the wire and the magnet push on each other with equal and opposite forces.

The size of the force depends on:

• the magnetic flux density (field strength) $B$;
• the current $I$ in the wire;
• the length $l$ of wire inside the field.

The force is largest when the wire is at right angles (90°) to the magnetic field, and is zero when the wire lies parallel to the field.

To get the maximum, steady force in a device, the wire is arranged perpendicular to the field lines. If the current or the field is reversed, the direction of the force reverses too.

(Higher Tier only) Direction and size of the motor-effect force.

To find the direction of the force, use Fleming's left-hand rule. Hold the thumb and first two fingers of your left hand at right angles to each other:

Finger	Represents
First finger	Field (N to S)
Second finger	Current
Thumb	Motion (force)

To find the size of the force on a conductor at right angles to the field:

$F=BIl$

where $F$ is the force in newtons (N), $B$ is the magnetic flux density in tesla (T), $I$ is the current in amperes (A), and $l$ is the length of the conductor in the field in metres (m).

This equation is given on the Physics equation sheet, so you do not need to memorise it, but you must be able to use and rearrange it.

Worked example — a 0.05 m length of wire carries a current of 3.0 A at right angles to a magnetic field of flux density 0.4 T. Find the force on the wire.

$F=BIl=0.4\times 3.0\times 0.05=0.06\text{N}$

The force on the wire is 0.06 N.

Worked example (rearranging) — a wire of length 0.20 m in a field feels a force of 0.12 N when a current of 2.0 A flows. Find the magnetic flux density.

$B=\frac{F}{Il}=\frac{0.12}{2.0\times 0.20}=\frac{0.12}{0.40}=0.3\text{T}$

The magnetic flux density is 0.3 T.

1. Using the wrong hand

The motor effect uses the left hand. The right hand belongs to the generator effect (induced current). Mixing them up gives the force in the wrong direction.

2. Muddling the fingers in Fleming's rule

First finger = Field, seCond finger = Current, thuMb = Motion (force). Keep all three at right angles to each other, or the directions come out wrong.

3. Forgetting the field runs north to south

In Fleming's rule the first finger points along the field, which means from the north pole to the south pole. Pointing it the wrong way reverses the predicted force.

4. Wrong angle for F = BIl

The equation $F=BIl$ applies when the wire is at right angles to the field. If the wire is parallel to the field the force is zero, and at other angles the force is smaller.

5. Unit slips in the calculation

$B$ is in tesla, $I$ in amperes and $l$ in metres. A length given in centimetres must be converted to metres first (0.05 m, not 5), or the answer will be a hundred times too large.