# The Motor Effect

> Why a wire carrying a current is pushed sideways in a magnetic field, and why two current-carrying wires attract or repel.

From HSC Physics on WhizzNotes, free study notes for NSW students: https://whizznotes.com/physics/the-motor-effect/. Updated 2 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The jumping wire
In 1821, Michael Faraday hung a loose wire so its bottom end dipped into a bowl of mercury, with a bar magnet standing up in the middle. When he switched on the current, the wire began to swing round and round the magnet, and kept going as long as the current flowed.

It was the world's first electric motor. It did nothing useful, but Faraday had shown something huge: electricity and magnetism together can make **movement**. Every fan, drill and electric car uses the push he saw that day.

**In short:** The motor effect is the force on a wire carrying a current in a magnetic field: $F = nIlB\sin\theta$. The force is largest when the wire is at right angles to the field, and its direction comes from the right-hand palm rule.

## Current makes a magnetic field

A wire carrying a current is surrounded by a **magnetic field** of circles around the wire.

- **Right-hand grip rule**: grip the wire with your right thumb along the current. Your fingers curl the way the field goes.
- The field is stronger close to the wire and weaker further away.

## The motor effect

Put a current-carrying wire in an external magnetic field and it feels a **force**. This is the **motor effect**. The size of the force is:

$$F = nIlB\sin\theta$$

- $n$ = number of wires (1 for a single wire)
- $I$ = current (A)
- $l$ = length of wire inside the field (m)
- $B$ = magnetic field strength (T)
- $\theta$ = angle between the wire and the field

The force is biggest when the wire is **at right angles** to the field. A wire **parallel** to the field feels **no force**.

### Worked example: A wire in a field
A 0.30 m length of wire carries 4.0 A at right angles to a 0.25 T field.

$F = IlB = 4.0 \times 0.30 \times 0.25 = 0.30$ N.

## Which way is the force?

Use the **right-hand palm rule**:

- **Fingers** point along the field $B$ (north to south).
- **Thumb** points along the current $I$ (positive to negative, conventional current).
- **Palm** pushes in the direction of the force $F$.

The force is always at right angles to both the current and the field. Reverse the current **or** reverse the field and the force reverses. Reverse both and it stays the same.

### Watch out: Mixing up the rules
The **grip** rule gives the shape of the field around one wire. The **palm** rule gives the force on a wire (or moving charge) sitting in a field. Use the palm rule for every force question.

## Two parallel wires

Each wire sits in the magnetic field of the other, so each feels a force.

- Currents in the **same** direction: wires **attract**.
- Currents in **opposite** directions: wires **repel**.

The force per metre of wire is:

$$\frac{F}{l} = \frac{\mu_0}{2\pi}\frac{I_1 I_2}{r}$$

- $\mu_0 = 4\pi \times 10^{-7}$ N A⁻² (the magnetic constant), so $\dfrac{\mu_0}{2\pi} = 2 \times 10^{-7}$
- $r$ = distance between the wires (m)

By Newton's third law, the two wires push or pull on each other with **equal and opposite** forces, even if their currents are different.

### Worked example: Power cables
Two long parallel wires 5.0 cm apart carry 20 A and 30 A in the same direction.

$\dfrac{F}{l} = 2 \times 10^{-7} \times \dfrac{20 \times 30}{0.050} = 2.4 \times 10^{-3}$ N per metre, attractive.

## What changes the force between wires?

- Double one current: double the force.
- Double the distance: half the force (not a quarter: it is $\dfrac{1}{r}$, not $\dfrac{1}{r^2}$).

**Mind map**

```text
The Motor Effect
  Current makes a field
    Circles round the wire
    Right-hand grip rule
  Force on a wire
    F = nIlB sin θ
    Largest at 90°
    Zero when parallel
  Direction
    Right-hand palm rule
    Fingers B, thumb I, palm F
    Reverse I or B: force reverses
  Parallel wires
    Same direction: attract
    Opposite: repel
    F/l = μ₀I₁I₂ / 2πr
  Newton's third law
    Equal and opposite forces
```

### Year 11: Charges and wires are the same idea
A current is a stream of moving charges. Each charge feels $F = qvB\sin\theta$. Add up the forces on all the charges in a length of wire and you get $F = IlB\sin\theta$. That is why the same palm rule works for both.

### Year 12: Measuring fields and the ampere
**Current balance.** Place a horizontal wire on an electronic balance, inside a magnetic field. As the current rises, the balance reading changes by $IlB$. A graph of force against current is a straight line through the origin with gradient $lB$, so $B = \dfrac{\text{gradient}}{l}$.

**The ampere.** The old definition of one ampere was the current in two long parallel wires 1 m apart that gives a force of $2 \times 10^{-7}$ N per metre. It is built directly on the formula above.

**Three wires.** For a wire between two others, find the force from each neighbour separately (including direction), then add them as vectors.

**Wire at an angle.** If a wire crosses the field at an angle, only the part of it at right angles to $B$ counts. For a bent wire, use the straight-line distance across the field between the points where it enters and leaves.

**Balancing forces.** A rod hanging from two strings in a field, with the magnetic force upwards: $2T + IlB = mg$. If the force were downwards, $2T = mg + IlB$.

**Force makes acceleration.** A rod of mass $m$ across rails carrying current $I$ in a field $B$ starts to accelerate at $a = \dfrac{IlB}{m}$ (ignoring friction). Two wires on trolleys pushed apart by $F = \dfrac{\mu_0}{2\pi}\dfrac{I_1 I_2}{r}l$ each accelerate at $\dfrac{F}{m}$.

**Between two wires.** With equal currents in the **same** direction, the two fields at the midpoint point opposite ways and cancel, so the field there is zero. With opposite currents, they add.

**AC in series.** If two parallel wires are connected so the current flows out along one and back along the other, the currents are always opposite, even as the AC reverses. So the wires always repel, with a force that pulses.

**Beams of charges.** A beam of electrons is a current in the opposite direction to the electrons' motion. Electrons moving in the same direction as the current in a nearby wire act like an opposite current, so the beam is pushed away from the wire.

**A balance that does not start at zero.** If the force against current graph is straight but does not pass through the origin, the gradient still gives $lB$. The intercept is a reading that has nothing to do with the current, such as the balance not being zeroed (a systematic error).

## Quick summary

- A current-carrying wire in a magnetic field feels a force: $F = nIlB\sin\theta$.
- The force is biggest when the wire is at 90° to the field, and zero when parallel.
- Direction: right-hand palm rule (fingers $B$, thumb $I$, palm $F$).
- Parallel wires attract if their currents are in the same direction and repel if opposite.
- Force between wires: $\dfrac{F}{l} = \dfrac{\mu_0}{2\pi}\dfrac{I_1 I_2}{r}$. The forces are equal and opposite.

## Quiz

Try these questions from the chapter quiz.

1. A wire carrying a current is placed in a magnetic field. What is this effect called?
   - A. The generator effect
   - B. The motor effect
   - C. Induction
   - D. The photoelectric effect
   - Answer: B. The motor effect. A force on a current-carrying wire in a magnetic field is the motor effect.

2. A wire carries 2.0 A at right angles to a 0.50 T field. The length in the field is 0.40 m. The force is:
   - A. 0.40 N
   - B. 1.6 N
   - C. 2.5 N
   - D. 0.10 N
   - Answer: A. 0.40 N. F = IlB = 2.0 × 0.40 × 0.50 = 0.40 N.

3. A wire lies parallel to a magnetic field. The force on it is:
   - A. Largest
   - B. Zero
   - C. Half the maximum
   - D. Upwards
   - Answer: B. Zero. sin 0° = 0, so a wire parallel to the field feels no force.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/physics/the-motor-effect/#quiz