Magnetic Force Simulator
Watch a charged particle move through a magnetic field. Adjust charge, velocity, and field strength to see the Lorentz force and circular orbit.
Magnetic Force on a Charged Particle
When a charged particle moves through a magnetic field, it experiences the Lorentz force F = qv × B. This force is perpendicular to both the velocity and the field, causing circular motion called cyclotron motion.
Cyclotron Radius
The radius of the circular orbit depends on mass, speed, charge, and field: r = mv/(|q|B). Heavier or faster particles orbit in larger circles; stronger fields create tighter orbits.
Key Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| q | Charge | μC | Charge of the particle (positive or negative) |
| v | Speed | Mm/s | Initial speed of the particle |
| B | Magnetic field | T | Uniform magnetic field strength (into page) |
| m | Mass | amu | Particle mass (fixed at 1 amu ≈ proton mass) |
| r | Cyclotron radius | m | r = mv/(|q|B) |
| T | Period | ns | T = 2πm/(|q|B) |
| f | Cyclotron frequency | MHz | f = |q|B/(2πm) |
Direction of Motion
For B into the page (×), a positive charge moving right feels a downward force (v × B = right × into-page = down). The particle curves into a clockwise circle. A negative charge curves in the opposite direction.
Key Formulas
| Formula | Description | Notes |
|---|---|---|
| F = qvB sin θ | Lorentz force magnitude | θ = 90° when v ⊥ B (max force) |
| r = mv/(|q|B) | Cyclotron radius | Larger v or m → larger orbit; larger q or B → smaller orbit |
| T = 2πm/(|q|B) | Orbital period | Independent of speed — basis of cyclotron accelerators |
| f = |q|B/(2πm) | Cyclotron frequency | Also independent of speed (for non-relativistic particles) |
Frequently Asked Questions
Why does a charged particle move in a circle in a magnetic field?
The Lorentz force qv×B is always perpendicular to the velocity, providing centripetal acceleration without changing the particle's speed. This constant redirection causes circular motion.
What is cyclotron frequency?
f = |q|B/(2πm). It depends only on the charge-to-mass ratio and field strength, not on speed — this is the principle behind cyclotron particle accelerators.
Does the magnetic force do work on the particle?
No. Since the force is always perpendicular to the velocity (and hence to displacement), the work done W = F·d = 0. The particle's kinetic energy and speed remain constant.
What happens if the charge is negative?
A negative charge experiences a force opposite to q(v×B). If a positive charge circles clockwise, a negative charge of equal magnitude circles counterclockwise with the same radius and period.