Magnetism and Moving Charges · 磁性与运动电荷
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| right-hand rule/raɪt hænd ruːl/ | 右手定则 | yòu shǒu dìng zé |
A magnet ignores a still charge but shoves a moving one sideways
- Place a charge at rest near a magnet — nothing happens.
- Send it flying across the field — it swerves to the side.
- The magnetic force acts only on a moving charge.
- And it pushes at right angles to the motion, not along it.
磁体不理会静止的电荷,却把移动的电荷推向侧面
- 把一个电荷静止放在磁体旁——什么也不发生。
- 让它飞越磁场——它就向侧面拐弯。
- 磁力只作用在移动的电荷上。
- 而且它以直角推动,与运动垂直,不沿着运动。
A magnetic field exerts a force on a charge only when the charge is: · 磁场仅对正在____的电荷施加力。
The magnetic force $F = qvB$ needs a nonzero velocity. · 磁场力$F = qvB$需要非零速度。
The force law: F = qvB
- The magnetic force is $F = qvB\sin\theta$, where $\theta$ is the angle between $\vec v$ and $\vec B$.
- It is maximum when the charge moves across the field ($\theta = 90^\circ$).
- It is zero when the charge moves along the field ($\theta = 0$).
- A faster charge or a stronger field gives a bigger push.
力的定律:F = qvB
- 磁力是 $F = qvB\sin\theta$,其中 $\theta$ 是 $\vec v$ 与 $\vec B$ 之间的夹角。
- 当电荷横越磁场时它最大($\theta = 90^\circ$)。
- 当电荷沿磁场移动时它为零($\theta = 0$)。
- 更快的电荷或更强的场给出更大的推力。
Force on a current · 电流所受的力
Set the field and current directions and use the right-hand rule to predict the force. · 设置磁场和电流方向，并使用右手定则预测受力。
A $3\ \text{C}$ charge moves at $4\ \text{m/s}$ across a $2\ \text{T}$ field ($\theta = 90^\circ$). Find $F$ (in N). · 一个$3\ \text{C}$电荷以$4\ \text{m/s}$的速度垂直穿过$2\ \text{T}$磁场（$\theta = 90^\circ$）。求$F$（单位为N）。
$F = qvB = 3 \times 4 \times 2 = 24\ \text{N}$.
A charge moving exactly along the field ($\theta = 0$) feels no magnetic force. · 一个电荷完全沿磁场方向运动（$\theta = 0$）时不受磁场力。
$\sin 0 = 0$, so $F = qvB\sin\theta = 0$. · $\sin 0 = 0$，所以 $F = qvB\sin\theta = 0$。
The right-hand rule sets the direction
- The force is perpendicular to both the velocity and the field.
- Point your fingers along $\vec v$, curl them toward $\vec B$: the thumb gives the force (right-hand rule 右手定则).
- For a negative charge, the force is the opposite way.
- That is why the two are always at right angles to the motion.
右手定则给出方向
- 力垂直于速度和场两者。
- 手指指向 $\vec v$,弯向 $\vec B$:拇指给出力(右手定则)。
- 对负电荷,力是相反方向。
- 这就是为什么两者总是与运动成直角。
The direction of the magnetic force is found with the ____-hand rule. · 磁场力的方向通过____手定则确定。
The right-hand rule gives the force on a positive charge. · 右手定则给出正电荷所受的力。
A sideways force makes a circle
- A force always perpendicular to $\vec v$ can only turn the charge, not speed it up.
- So a charge in a uniform field moves in a circle.
- The radius is $r = \dfrac{mv}{qB}$ — faster or heavier means a wider circle.
- This is how mass spectrometers and particle accelerators bend beams.
侧向力使电荷绕圈
- 一个总是垂直于 $\vec v$ 的力只能让电荷转向,不能让它加速。
- 所以均匀场中的电荷做圆周运动。
- 半径是 $r = \dfrac{mv}{qB}$——更快或更重意味着更大的圆。
- 这就是质谱仪和粒子加速器如何弯曲束流。
Select all · 所有 true statements about the magnetic force on a charge. · 选择关于电荷所受磁力的所有正确陈述。
Needs motion, perpendicular, no work. It never speeds the charge up. · 需要运动，垂直，不做功。它永远不会使电荷加速。
The magnetic force does no work
- Because $\vec F \perp \vec v$, the force never adds to the speed.
- It changes only the direction of motion, not the kinetic energy.
- So a magnetic field can steer a charge but never make it faster.
- Speeding up needs an electric field, not a magnetic one.
磁力不做功
- 因为 $\vec F \perp \vec v$,力从不增加速率。
- 它只改变运动的方向,不改变动能。
- 所以磁场能引导电荷,却永远不能让它更快。
- 加速需要电场,不是磁场。
The magnetic force on a moving charge: · 运动电荷受到的磁场力：
Since $F \perp v$, it does no work — only the direction changes. · 由于$F \perp v$，它不做功 —— 仅改变方向。
A charge of $2\ \text{C}$ moves at $3\ \text{m/s}$ across a $0.5\ \text{T}$ field ($\theta = 90^\circ$).
- $F = qvB = 2 \times 3 \times 0.5 = 3\ \text{N}$.
- The force is perpendicular to the velocity, so the charge curves.
一个 $2\ \text{C}$ 的电荷以 $3\ \text{m/s}$ 横越一个 $0.5\ \text{T}$ 的场($\theta = 90^\circ$)。
- $F = qvB = 2 \times 3 \times 0.5 = 3\ \text{N}$。
- 力垂直于速度,所以电荷弯曲。
The magnetic force does no work — it only bends the path, never changes the speed. So "the magnetic field speeds up the charge" is always wrong. And a charge moving along the field ($\theta = 0$) feels no force at all.
磁力不做功——它只弯曲路径,永不改变速率。所以"磁场使电荷加速"永远是错的。而且沿场($\theta = 0$)移动的电荷完全不受力。
A magnetic field pushes only a moving charge: $F = qvB\sin\theta$, perpendicular to both $\vec v$ and $\vec B$ (right-hand rule). The force does no work, so it bends the path into a circle of radius $r = mv/qB$ without changing the speed.
磁场只推动移动的电荷:$F = qvB\sin\theta$,垂直于 $\vec v$ 和 $\vec B$(右手定则)。力不做功,所以它把路径弯成半径 $r = mv/qB$ 的圆而不改变速率。