Lorentz Force Calculator
Enter charge, velocity, magnetic and electric fields to compute the Lorentz force F = q(E + v×B).
Input Data
Results
At a glance:The Lorentz force is the total force on a point charge in electromagnetic fields: F = q·(E + v×B), where E is the electric field, B the magnetic field and v the charge's velocity. The magnetic part F_B = q·v×B has magnitude q·v·B·sinθ (θ angle between v and B) and is perpendicular to both v and B — it changes direction but not speed of the charge. The electric part F_E = qE is parallel to E. Combining: F = qE + qvB sinθ. The force curves charged-particle trajectories (cyclotron motion) and underlies motors, mass spectrometers and the Hall effect. This tool gives F_B, F_E and the vector total; 'equivalent mass' interprets F/a as an effective inertia if an acceleration is implied.
Formula
Lorentz force: F = q·(E + v×B)
Magnetic: F_B = q·v·B·sinθ
Electric: F_E = q·E
$$\mathbf{F} = q\left(\mathbf{E} + \mathbf{v} \times \mathbf{B}\right)$$$$F_B = q\,v\,B\,\sin\theta$$How to Use
- Enter charge q, velocity v, magnetic field B and angle θ.
- Optionally enter electric field E.
- The calculator returns F_B, F_E, total F and equivalent mass.
Case Studies
Electron in a field
q = 1.6e-19 C, v = 1e6 m/s, B = 0.1 T, θ=90°.
F_B = 1.6e-19×1e6×0.1 = 1.6e-14 N.
Curves the electron into circular motion.
FAQ
Why does the magnetic force not change speed?
F_B = qv×B is always perpendicular to v, so it does no work (power F_B·v = 0); it only bends the path, producing circular/helical motion at constant speed.
What if there is no electric field?
Then F = qv×B only; a charge moving parallel to B (θ=0) feels zero force, while perpendicular motion gives the maximum qvB and uniform circular motion.
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References
Content review: Calculatorism Editorial Team. Results are for reference only; please refer to the relevant authorities for the official figures.