Magnetism and Moving Charges
ВведеноA 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.
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.
A field in space
See the magnetic field a magnet creates — the field a moving charge would cut across.
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 $\text{N}$?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
$F = qvB = 2 \times 3 \times 4 = 24\ \text{N}$.
The magnetic force on a moving charge is directed:
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
The force is perpendicular to both the velocity and the field.
A charge moving exactly along the field lines feels a force of:
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Moving along the field gives no sideways force; the force needs motion across the field.
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.
Because it acts perpendicular to the motion, the magnetic force does no ____.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
A perpendicular force does no work, so the speed is unchanged.
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.
A stationary charge in a magnetic field feels the maximum magnetic force.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
False. The magnetic force needs motion: $F = qvB\sin\theta$ is zero when $v = 0$.
Select все true statements about the magnetic force on a charge.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
The force needs motion, is perpendicular, and bends the path into a circle — but does no work, so it never changes the speed.
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.
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.
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.
Write from a magnetic force of 30 N
- A 5 C charge moves at 2 m/s at right angles to a 3 T field.
- Find the magnetic force.
A charge of 5 C moves at 2 m/s at right angles to a magnetic field of 3 T. What magnetic force does it feel, in newtons?
5 times 2 times 3 is 30.
What is the magnetic force?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
Charge times speed times field is 30 N at right angles. Other options — 24 N (the lesson force); 0 N (the force on a charge that is not moving).