Magnetism and Moving Charges
Introduced| English |
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| right-hand rule/raɪt hænd ruːl/ |
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.
A magnetic field exerts a force on a charge only when the charge is:
The magnetic force $F = qvB$ needs a nonzero velocity.
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.
Force on a current
Set the field and current directions and use the right-hand rule to predict the force.
A $3\ \text{C}$ charge moves at $4\ \text{m/s}$ across a $2\ \text{T}$ field ($\theta = 90^\circ$). Find $F$ (in N).
$F = qvB = 3 \times 4 \times 2 = 24\ \text{N}$.
A charge moving exactly along the field ($\theta = 0$) feels no magnetic force.
$\sin 0 = 0$, so $F = qvB\sin\theta = 0$.
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.
The direction of the magnetic force is found with the ____-hand rule.
The right-hand rule gives the force on a positive charge.
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.
Select all true statements about the magnetic force on a charge.
Needs motion, perpendicular, no work. It never speeds the charge up.
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.
The magnetic force on a moving charge:
Since $F \perp v$, it does no work — only the direction changes.
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.
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.
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.