Magnetic Force Calculator
F = qvB·sinθ, with the radius of the curl.
F = qvB·sinθ, with the radius of the curl.
An electron or proton is 1.602e-19 C.
Fridge magnet 0.005, MRI 1.5–3, strongest lab magnets about 45.
Optional — gives the radius of the circular path. Proton 1.673e-27, electron 9.109e-31.
Magnetic force
8.0109e-14 N
Perpendicular — the maximum possible force
F = qvB·sin θ, and the force is perpendicular to both the velocity and the field. That perpendicularity means a magnetic field changes a charge's direction without ever changing its speed — it does no work at all. So the path curls into a circle rather than accelerating away, and the orbital period turns out to be independent of speed. That is the principle behind the cyclotron: a fixed-frequency drive keeps working as the particle speeds up. A charge moving exactly along the field feels no force whatsoever, which is why charged particles spiral along Earth's field lines to the poles rather than being deflected uniformly — and why aurorae appear where they do.
How the Magnetic Force Calculator works
Enter charge, speed, field and angle for the magnetic force, plus the radius and period of the circular path if you supply a mass. A magnetic field does no work. It turns a charge without ever speeding it up.
Also known as: lorentz force calculator · force on a moving charge · f = qvb calculator · radius of circular motion in a magnetic field
Where to go next
The Magnetic Force question rarely arrives on its own. These are the ones that usually come with it:
- Coulomb's Law Calculator — Electrostatic force, and how far it beats gravity.
- Electric Field Calculator — Point charge or parallel plates, in N/C and V/m.
- Inductance Calculator — Reactance at frequency, and where L and C cancel.
- Speed Distance Time Calculator — Any one of the three from the other two, in four units.
Frequently asked questions
What is the formula for magnetic force on a charge?
F = qvB·sin θ, where θ is the angle between the velocity and the field. It is maximum at 90° and exactly zero when the charge moves along the field.
Why does a magnetic field do no work?
Because the force is always perpendicular to the velocity. It changes direction without changing speed, so no energy is transferred — which is why the path curls into a circle rather than accelerating.
What is the radius of the circular path?
r = mv/qB. Heavier or faster particles curve less; stronger fields curve them more. That relationship is exactly how a mass spectrometer separates isotopes.
Why do aurorae appear near the poles?
Because charged particles feel no force moving along a field line, so they spiral down Earth's field lines rather than being deflected uniformly, and those lines converge at the poles.
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Related calculators
Coulomb's Law Calculator
Electrostatic force, and how far it beats gravity.
OpenElectric Field Calculator
Point charge or parallel plates, in N/C and V/m.
OpenInductance Calculator
Reactance at frequency, and where L and C cancel.
OpenSpeed Distance Time Calculator
Any one of the three from the other two, in four units.
Open