Charged Particles Moving in a Magnetic Field
A charge crossing a magnetic field feels a force BQv that stays at right angles to its velocity, so the path curves into a circle. Setting BQv equal to mv squared over r gives the radius.
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 steer charged particles by bending their paths in a magnetic field. A charge crossing the field feels F equals B Q v, sideways to both its motion and the field. Positive charges bend one way and negative charges bend the opposite way in the same field. Motion parallel to the field feels nothing at all.
Crossing a uniform field at right angles, the charge travels in a circle. A fixed sideways push is exactly what circular motion needs. Setting B Q v equal to m v squared over r gives r equals m v over B Q. Fast or heavy swings wide, while highly charged curls tight.
The push stays across the motion, so it turns the particle without doing work. Speed never changes and kinetic energy is untouched. The field steers but never pays: direction changes, pace stays.
Bend charges sideways by sign, size the circle by momentum over charge, and keep the speed untouched.
2 · Watch
Take it off screen
Where it sits
Learn first
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.