Force on a Current and the Electric Motor: Quick Revision

A brief note on Force on a Current and the Electric Motor. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• A wire with a current in a magnetic field feels a force, at right angles to both the field and the current.
• The force is largest at right angles to the field ($F = BIL$) and zero along the field.
• Fleming's left-hand rule: forefinger for the field, middle finger for the current, thumb for the force.
• In a DC motor, the two sides of a coil feel opposite forces, so it turns. The split ring reverses the current every half turn, and fixed brushes carry the current in.
• A galvanometer turns in proportion to the current. A loudspeaker turns a changing current into sound.

The facts at a glance

A worked example

A wire $0.12\ \text{m}$ long carries $3.5\ \text{A}$ at right angles to a field of $0.5\ \text{T}$. Find the force on it, and the force when it makes $30^\circ$ with the field.

1. At right angles. $F = BIL = 0.5\ \text{T} \times 3.5\ \text{A} \times 0.12\ \text{m} = 0.21\ \text{N}$.
2. At $30^\circ$. $F = 0.21\ \text{N} \times \sin 30^\circ = 0.21\ \text{N} \times 0.5 = 0.105\ \text{N}$.

Practice with new numbers

A program to try

The program works out the force at two angles, and the turning effect of a coil in the same field.

Mistakes to avoid

• Using the right hand for the force on a current. The left hand is for motors; the right hand is for generators.
• Using $\cos\theta$ for the force when $\theta$ is the angle between the wire and the field. It is $\sin\theta$.
• Saying the brushes turn. The split ring turns with the coil; the brushes stay still.
• Reversing both the current and the field and expecting the motor to turn the other way. It turns the same way.

Check yourself

1. A field points to the right. A wire carries a current out of the page. Which way is the force on it?

2. A coil of $120$ turns, each of area $0.002\ \text{m}^2$, carries $2.5\ \text{A}$ in a field of $0.4\ \text{T}$. What is its largest turning effect?

3. What does the split ring of a DC motor do, and why?

4. A galvanometer turns $60^\circ$ for $15\ \text{mA}$. What current turns it $24^\circ$?