Force on a current-carrying conductor
| English | Chinese | Pinyin |
|---|---|---|
| motor effect | 电动机效应 | diàn dòng jī xiào yìng |
| magnetic flux density | 磁通密度 | cí tōng mì dù |
| tesla | 特斯拉 | tè sī lā |
| Fleming's left-hand rule | 弗莱明左手定则 | fú lái míng zuǒ shǒu dìng zé |
The wire that jumps
- Put a current-carrying wire in a magnetic field and it suddenly jumps sideways.
- This is the motor effect 电动机效应 — 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.
Concentric circular field lines around a long straight wire carrying current into the page
Feel the force on the wire
A current in a magnetic field feels a force F = BIL at right angles to both — reverse the current or flip the magnet and the force jumps the other way.
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 $F = BIL$).
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.
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 磁通密度
- This also defines $B$: $B = \dfrac{F}{IL}$ (wire at right angles).
- Unit: the tesla 特斯拉 ($1\ \text{T} = 1\ \dfrac{\text{N}}{\text{A}\cdot\text{m}}$).
Fleming's left-hand rule 弗莱明左手定则: thumb is force or motion, first finger is field, second finger is current, all at right angles
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).
A current-carrying slab in a field into the page develops a Hall voltage across its faces as charges build up
In Fleming's left-hand rule, the thumb shows the:
First finger = Field, second finger = Current, thumb = force/Motion.
You've got it
- 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)