Magnetic Force Calculator
Enter charge, velocity and magnetic field to compute the magnetic force F = q·v·B·sinθ on a moving charge.
Input Data
Results
At a glance:The magnetic part of the Lorentz force on a moving charge is F = q·(v×B), with magnitude F = q·v·B·sinθ, where θ is the angle between velocity v and magnetic field B. The force is perpendicular to both v and B, so it changes the charge's direction but not its speed (does no work). Maximum at θ=90° (F = qvB), zero when v∥B (θ=0 or 180°). It produces circular motion for a charge entering B perpendicularly (radius r = mv/(qB)). This is the basis of cyclotrons, mass spectrometers and the Aurora. This tool computes F from q, v, B and θ.
Formula
F = q·v·B·sinθ
Circular radius: r = m·v/(q·B)
$$F = q\,v\,B\sin\theta$$How to Use
- Enter the charge q (C).
- Enter velocity v (m/s), field B (T) and angle θ (°).
- The calculator returns the force F.
Case Studies
Proton in a field
q = 1.6e-19 C, v = 5e6 m/s, B = 0.2 T, θ=90°.
F = 1.6e-19×5e6×0.2 = 1.6e-13 N.
Curves into a circle of radius r = mv/qB.
FAQ
Why doesn't magnetic force do work?
Because F ⊥ v always, the power F·v = 0; the field only steers the charge, changing direction, not kinetic energy.
When is the force zero?
When v is parallel or antiparallel to B (θ=0° or 180°), sinθ=0, so no magnetic force — the charge travels straight.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.