Magnetism and Moving Charges · 磁性与运动电荷
A magnet can bend a beam of moving charges
- In an old TV tube, magnets steer a beam of electrons to paint the picture.
- A magnetic field grabs a moving charge and shoves it sideways.
- The force is strange: it acts perpendicular to both the motion and the field.
- This sideways magnetic force runs motors, mass spectrometers and particle detectors.
磁铁能让运动电荷的束流拐弯
- 在老式电视显像管里,磁铁引导一束电子来绘制画面。
- 磁场抓住运动的电荷,把它往旁边一推。
- 这个力很奇怪:它作用在垂直于运动和场的方向上。
- 这个侧向磁力驱动电动机、质谱仪和粒子探测器。
The magnetic force on a charge
- A charge $q$ moving at speed $v$ across a field $B$ feels a force $F = qvB$.
- The force is perpendicular to both the velocity and the field.
- A charge moving along the field lines feels no force at all.
- The force is largest when the charge moves at right angles to the field.
电荷所受的磁力
- 一个以速率 $v$ 横越场 $B$ 运动的电荷 $q$ 感到力 $F = qvB$。
- 这个力垂直于速度和场两者。
- 沿磁感线方向运动的电荷完全不受力。
- 当电荷与场成直角运动时,力最大。
A field in space · 空间中的磁场
See the magnetic field a magnet creates — the field a moving charge would cut across. · 观察磁体产生的磁场——即运动电荷会切割的磁场。
A $2\ \text{C}$ charge moves at $3\ \tfrac{\text{m}}{\text{s}}$ across a $4\ \text{T}$ field (right angles). What force does it feel, in $\text{N}$? · 一个$2\ \text{C}$电荷以速度$3\ \tfrac{\text{m}}{\text{s}}$穿过磁场$4\ \text{T}$（垂直）。它受到的力是多少，单位为$\text{N}$？
$F = qvB = 2 \times 3 \times 4 = 24\ \text{N}$.
The magnetic force on a moving charge is directed: · 运动电荷所受的磁力方向为：
The force is perpendicular to both the velocity and the field. · 该力垂直于速度和磁场两者。
A charge moving exactly along the field lines feels a force of: · 完全沿磁感线运动的电荷受到的力为：
Moving along the field gives no sideways force; the force needs motion across the field. · 沿磁场运动不产生侧向力；力需要垂直于磁场的运动分量。
The right-hand rule
- Point your right hand's fingers along $v$, curl toward $B$; your thumb gives the force (for a positive charge).
- For a negative charge, the force is the opposite way.
- Because the force is always sideways, it changes the charge's direction but not its speed.
- A charge moving across a uniform field therefore travels in a circle.
右手定则
- 让右手四指沿 $v$,弯向 $B$;拇指给出力的方向(对正电荷)。
- 对负电荷,力的方向相反。
- 因为力总是侧向的,它改变电荷的方向而非速率。
- 因此横越均匀场运动的电荷沿圆运动。
Because it acts perpendicular to the motion, the magnetic force does no . · 因为它垂直于运动方向，所以磁力不做。
A perpendicular force does no work, so the speed is unchanged. · 垂直方向的力不做功，因此速率保持不变。
Circular motion in a field
- The sideways force acts like a centripetal force, bending the path into a circle.
- Faster charges or weaker fields make bigger circles.
- This is how a mass spectrometer sorts particles by mass and charge.
- The magnetic force does no work (it is perpendicular to the motion), so speed stays constant.
场中的圆周运动
- 侧向力起着向心力的作用,把路径弯成一个圆。
- 更快的电荷或更弱的场造成更大的圆。
- 这就是质谱仪按质量和电荷分选粒子的方式。
- 磁力不做功(它垂直于运动),所以速率保持不变。
A stationary charge in a magnetic field feels no magnetic force. · 静止在磁场中的电荷不受磁力。
The magnetic force needs motion: $F = qvB$ is zero when $v = 0$. · 磁力需要运动： $F = qvB$ 在 时为零 $v = 0$.
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。
The force needs motion, is perpendicular, and bends the path into a circle — but does no work, so it never changes the speed. · 力需要运动，是垂直的，并将路径弯曲成圆形——但不做功，因此永远不会改变速率。
The magnetic force needs the charge to be moving — a stationary charge feels no magnetic force. And the force is perpendicular to the velocity, so it does no work and never changes the charge's speed, only its direction.
磁力需要电荷在运动——静止的电荷不受磁力。而且力垂直于速度,所以它不做功,永远不改变电荷的速率,只改变方向。
A charge of $q = 2\ \text{C}$ moves at $v = 3\ \tfrac{\text{m}}{\text{s}}$ across a field of $B = 4\ \text{T}$ (at right angles).
- $F = qvB = 2 \times 3 \times 4 = 24\ \text{N}$, perpendicular to the motion.
Line the velocity up along the field instead, and the force drops to zero.
一个 $q = 2\ \text{C}$ 的电荷以 $v = 3\ \tfrac{\text{m}}{\text{s}}$ 横越 $B = 4\ \text{T}$ 的场(成直角)。
- $F = qvB = 2 \times 3 \times 4 = 24\ \text{N}$,垂直于运动。
若让速度沿场排列,力就降到零。
A moving charge in a magnetic field feels a force $F = qvB$, perpendicular to both its velocity and the field (use the right-hand rule). A charge moving along the field feels no force. The force does no work — it bends the path into a circle without changing the speed.
运动的电荷在磁场中感到力 $F = qvB$,垂直于它的速度和场两者(用右手定则)。沿场运动的电荷不受力。这个力不做功——它把路径弯成圆而不改变速率。