Particle Accelerators

Overview

This lesson extends magnetic force from current-carrying wires to individual charged particles. You will use F = BQv sin theta, direction rules, circular motion ideas, and velocity selection.

What You Need to Know

• A moving charge in a magnetic field can experience a force.
• The force is given by F = BQv sin theta, where theta is the angle between velocity and field.
• The force is perpendicular to the velocity, so it can provide the centripetal force for circular motion.
• A stationary charge does not experience a magnetic force.
• For a particle entering a uniform field at right angles, the magnetic force changes direction but does not change the speed.
• Velocity selectors use balanced electric and magnetic forces so only particles with a specific speed pass through undeflected.

How to Work Through It

1. Start with force directions for positive and negative charges.
2. Practise F = BQv sin theta calculations, including charge in coulombs.
3. Link magnetic force to centripetal force for circular paths.
4. Use balanced force diagrams to explain velocity selection.

Check Your Understanding

• Why does a particle move in a circle when velocity is perpendicular to a uniform magnetic field?
• What changes when the particle charge is negative?
• Why does the magnetic force do no work on the particle in uniform circular motion?
• How does a velocity selector reject particles that are too fast or too slow?

Common Mistakes

• Forgetting that Q must be in coulombs.
• Using the direction rule for conventional current without adjusting for electron motion.
• Saying the magnetic field speeds the particle up when the force is perpendicular to velocity.
• Treating F = BQv as valid when the velocity is not perpendicular to the field.

Next Steps

• Keep magnetic force and centripetal force ideas available for mixed calculations.
• Use this charge-motion model before studying the Hall effect.