Force on a current-carrying conductor
The wire that jumps
- Put a current-carrying wire in a magnetic field and it suddenly jumps sideways.
- This is the motor effect — the force behind every electric motor.
- Its size and direction follow two simple rules.
The force
- $F = BIL\sin\theta$, where $\theta$ is the angle between the wire and the field.
- Largest at right angles ($F = BIL$); zero when the wire lies along the field.
Practice
The force on a current-carrying wire in a magnetic field is:
Largest when the wire is perpendicular to the field ($\sin 90^{\circ} = 1$, so $F = BIL$).
Practice
The force on the wire is zero when it lies along the field.
With the wire parallel to the field, $\theta = 0$ and $\sin\theta = 0$, so there is no force.
Practice
A $0.10\ \text{m}$ wire carries $2.0\ \text{A}$ at right angles to a $0.50\ \text{T}$ field. What is the force?
$F = BIL = 0.50 \times 2.0 \times 0.10 = 0.10\ \text{N}$.
Magnetic flux density
- This also defines $B$: $B = \dfrac{F}{IL}$ (wire at right angles).
- Unit: the tesla ($1\ \text{T} = 1\ \dfrac{\text{N}}{\text{A}\cdot\text{m}}$).
Practice
Magnetic flux density is measured in the ____.
$1\ \text{T} = 1\ \dfrac{\text{N}}{\text{A}\cdot\text{m}}$ — the force per unit current per unit length.
Fleming's left-hand rule
- Hold thumb and first two fingers at right angles on your left hand.
- First finger = Field, seCond finger = Current, thuMb = force (Motion).
Practice
In Fleming's left-hand rule, the thumb shows the:
First finger = Field, second finger = Current, thumb = force/Motion.
You've got it
Key idea
- force on a current: $F = BIL\sin\theta$ (max at right angles, zero along the field)
- flux density $B = \dfrac{F}{IL}$, in tesla
- direction from Fleming's left-hand rule (Field, Current, Motion)