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Magnetic force on a moving charge
Intermediate
Force perpendicular to velocity and field.
F = qv×BF = qv×B: perpendicular to both velocity and B, with magnitude qvB sinθ. It changes the direction but not the speed, so does no work.
An electron at 10⁶ m/s in 0.1 T: 1.6×10⁻¹⁴ N.
No force on a charge at rest or moving along B.
In more detail
A moving charge in a magnetic field experiences a force F = qvB sin θ, perpendicular to both velocity and field. The magnetic force does no work and changes only the direction of motion.
Real-world uses
- Mass spectrometers use this force to separate ions.
- Particle beams are steered with magnetic fields.
- Particle detectors use the magnetic force on moving charges to bend their paths and measure their momentum.
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Frequently asked questions
Why does the force act sideways?
Because it is the cross product of velocity and field, which is perpendicular to both.
Does the force speed up the particle?
No. It changes direction only, so the speed stays constant.
Does a magnetic field do work on a charge?
No. The force is always perpendicular to the velocity, so it changes the direction of motion but not the speed.
Related topics in Magnetism & Induction
Magnets and poles · Magnetic field lines · Earth's magnetic field · Circular motion in B field · Cyclotron frequency · Helical motion