Magnetic Force Calculator
Calculate the magnetic force on a moving charge or current-carrying conductor using the Lorentz force law.
The magnetic force is the component of the electromagnetic force that acts on a moving electric charge or current-carrying conductor when it is in a magnetic field. This force is described by the Lorentz force law and is fundamental to electric motors, generators, particle accelerators, and many other technologies.
Force on a Moving Charge
When a charged particle moves through a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field:
F = q × v × B × sin(θ)
Where:
- F = magnetic force (Newtons, N)
- q = electric charge (Coulombs, C)
- v = velocity of the particle (meters per second, m/s)
- B = magnetic field strength (Tesla, T)
- θ = angle between velocity vector and magnetic field vector
The force is maximum (θ = 90°) when velocity is perpendicular to the field, and zero (θ = 0°) when velocity is parallel to the field.
Force on a Current-Carrying Wire
A wire carrying current in a magnetic field experiences a force:
F = I × L × B × sin(θ)
Where:
- I = current (Amperes, A)
- L = length of the wire in the field (meters, m)
- B = magnetic field strength (Tesla, T)
- θ = angle between wire and field
This is the principle behind electric motors: current in the armature windings interacts with the motor’s magnetic field to produce rotational force (torque).
Magnetic Field Strength Reference
| Source | Field Strength |
|---|---|
| Earth’s magnetic field | 25–65 μT (microtesla) |
| Refrigerator magnet | ~5 mT (millitesla) |
| MRI scanner | 1.5–3 T |
| Neodymium magnet | 1–1.4 T (surface) |
| Strongest continuous field | 45 T (laboratory) |
Direction of the Force
The direction of the magnetic force is given by the right-hand rule: point fingers in the direction of velocity (or current), curl toward the magnetic field, and the thumb points in the direction of force (for positive charges).