Charged Particles Moving in a Magnetic Field
A particle moving at right angles to a uniform magnetic field experiences force of size B Q v, with Q as charge magnitude. The force stays perpendicular to velocity, producing a circle. Equating B Q v with m v squared / r gives r = (m v)/(B Q).
What a learner can do afterwards
- Gives the direction of the force on a positive and on a negative charge in the same field
- Derives r = mv over BQ and uses it to compare particles of different mass or charge
- Explains why a magnetic field changes a particle's direction but never its speed
1 · Read
Mass spectrometers bend charged particles' paths using magnetic fields. For motion at right angles to a field, the force size is F = B Q v, where Q is charge magnitude. The force is perpendicular to both velocity and field. Opposite charge signs give opposite force directions for the same velocity and field. Motion parallel to the field has no magnetic force.
A charge moving perpendicular to a uniform field follows a circle. Q is charge magnitude, not sign; m is mass, v speed and r radius. The force B Q v has constant size and points inward, perpendicular to motion. It supplies the centripetal force m v squared / r. Equating them gives r = (m v)/(B Q). With other quantities fixed, larger m or v increases r; larger Q or B decreases r. Changing +Q to -Q reverses bending but leaves Q and r unchanged.
The push stays across the motion, so it turns the particle without doing work. The direction changes, but speed and kinetic energy never change.
For motion perpendicular to a uniform field, charge sign sets force direction and r = (m v)/(B Q), with Q as charge magnitude. Magnetic forces do no work, so speed stays unchanged.
Original charged-particle lesson and questions written for Marble.
Original charged-particle readings and flashcards written for Marble. Linked videos are by khanacademymedicine; their licenses are unknown.
2 · Watch
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Where it sits
Where this leads
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