About the Magnetic Force Calculator
This magnetic force calculator finds the force a magnetic field exerts on a moving electric charge (F = |q|vB sin θ) or on a straight wire carrying a current (F = BIL sin θ). Pick a proton, electron or alpha particle — or enter any charge and mass — together with its speed, the field strength and the angle between the velocity and the field. For particles it also returns the radius of the circular path the force produces and the cyclotron frequency.
It is meant for physics students working on electromagnetism problems, teachers building examples about mass spectrometers, cyclotrons and electric motors, and hobbyists estimating the push on a conductor in a magnet gap. A chart shows how the force depends on the angle: it is greatest when the motion is perpendicular to the field and zero when it runs parallel.
The force is always perpendicular to both the velocity (or current) and the field, so it changes the direction of motion but never the speed. The direction follows the right-hand rule for positive charges and is reversed for negative charges such as electrons. The radius and frequency use non-relativistic mechanics, which is accurate for speeds well below the speed of light (under about 10% of c).
How to use the magnetic force calculator
- 1Choose a moving charge or a current-carrying wire.
- 2For a charge, pick a particle (or enter a custom charge and mass) and its speed.
- 3For a wire, enter the current and the length inside the field.
- 4Enter the field strength, its unit, and the angle between the motion and the field.
- 5Read the force, its direction and, for particles, the orbit radius and frequency.
Formula and method
The magnetic part of the Lorentz force on a charge q moving with velocity v through a field B is F = q v × B. Its magnitude is |q|vB sin θ, where θ is the angle between the velocity and the field, so the force is largest at 90° and vanishes when the charge moves along the field lines. A current is just a stream of moving charges, so a straight wire of length L carrying current I feels F = BIL sin θ.
Because the force is always perpendicular to the velocity, it does no work and only bends the path. Setting it equal to the centripetal force m v²/r gives the radius of the circle, r = mv⊥/(|q|B), and the cyclotron frequency f = |q|B/(2πm), which does not depend on speed. Particle masses and the elementary charge are CODATA values. The radius formula is non-relativistic.
- F
- Magnetic force (N)
- q
- Charge (C)
- v
- Speed (m/s)
- B
- Magnetic flux density (T); 1 T = 10,000 G
- θ
- Angle between velocity (or current) and field
- I
- Current (A)
- L
- Length of wire inside the field (m)
- r
- Radius of the circular or helical path (m)
- m
- Particle mass (kg)
- f
- Cyclotron frequency (Hz)
Worked examples
Proton at 1,000 km/s in a 0.5 T field
F = 1.602 × 10⁻¹⁹ × 10⁶ × 0.5 = 8.01 × 10⁻¹⁴ N. The proton circles with r = (1.6726 × 10⁻²⁷ × 10⁶) / (1.602 × 10⁻¹⁹ × 0.5) = 2.09 cm at a cyclotron frequency of 7.62 MHz.
Electron at 2 × 10⁷ m/s in a 1 mT field
F = 1.602 × 10⁻¹⁹ × 2 × 10⁷ × 0.001 = 3.20 × 10⁻¹⁵ N. Because the electron is so light, even this weak field bends it into a circle about 11.4 cm in radius — the principle behind old CRT televisions.
Wire carrying 10 A across a 0.2 T field
With the wire perpendicular to the field, F = 0.2 × 10 × 0.5 × sin 90° = 1 N, or 2 N for every metre of wire in the field.
The same wire at 30° to the field
Only the component of the current perpendicular to the field counts: F = 1 N × sin 30° = 0.5 N.
Frequently asked questions
What is the formula for magnetic force on a moving charge?+
F = |q| v B sin θ, where q is the charge, v the speed, B the field strength and θ the angle between the velocity and the field. In vector form F = q v × B, the magnetic part of the Lorentz force.
What is the Lorentz force?+
The Lorentz force is the total electromagnetic force on a charge: F = q(E + v × B). It combines the electric force qE, which acts even on stationary charges, and the magnetic force qv × B, which acts only on moving charges.
How do I find the direction of the magnetic force?+
Use the right-hand rule: point your fingers along the velocity (or current), curl them toward the field, and your thumb shows the force on a positive charge. For a negative charge such as an electron, the force points the opposite way.
Why does a magnetic field not change a particle’s speed?+
The magnetic force is always perpendicular to the velocity, so it does no work. It changes the direction of motion, making charged particles move in circles or helices, but the kinetic energy stays the same.
What is the force on a current-carrying wire?+
F = BIL sin θ, with B in tesla, I in amperes and L the length of wire inside the field in metres. This force is what turns electric motors and moves loudspeaker cones.
How do I convert gauss to tesla?+
One tesla equals 10,000 gauss, so 1 G = 0.0001 T. Earth’s field is about 0.25–0.65 G (25–65 µT), a fridge magnet roughly 50–100 G, and an MRI scanner 1.5–3 T.