Lorentz Magnetic Force
F = q · v · B · sin(θ)
Quick answer
This calculator solves F = q × v × B × sin(θ) for Force. With Charge 10 nC, Velocity 10 m/s, Flux Density 0.5 T, Angle v to B 45 °, the result is 0.03536 µN. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The magnetic part of the Lorentz force is the force on a charge moving through a magnetic field. It is maximum when the velocity is perpendicular to the field and zero when parallel. The force is always perpendicular to both the velocity and the field, which is why a uniform magnetic field makes charges move in circles rather than speeding them up. It underlies motors, Hall sensors, CRTs, and mass spectrometers.
Variables
- F — Magnetic force (N)
- q — Charge (C)
- v — Speed of the charge (m/s)
- B — Magnetic flux density (T)
- θ — Angle between velocity and field (degrees)
Practical Notes
The full Lorentz force adds the electric term qE. Because the magnetic force does no work (it is perpendicular to motion), it changes direction but not the kinetic energy of the charge.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| F | Force | N | µN, mN, N, kN |
| q | Charge | nC | pC, nC, µC, mC, C |
| vel | Velocity | m/s | mm/s, m/s, km/s |
| B | Flux Density | T | G, mT, T |
| theta | Angle v to B | ° | ° |
Step by step
- 1. What you know: Charge 10 nC, Velocity 10 m/s, Flux Density 0.5 T, Angle v to B 45 °
- 2. The relation: F = q × v × B × sin(θ)
- 3. Substitute: q = 10 nC, vel = 10 m/s, B = 0.5 T, theta = 45 °
- 4. Result: Force = 0.03536 µN
Worked examples
Minimum range
Given: Charge 100 pC, Velocity 10 mm/s, Flux Density 10 G, Angle v to B 1.5 °
Result: Force = 2.62 × 10⁻¹¹ µN
Low range
Given: Charge 1 nC, Velocity 100 mm/s, Flux Density 10 mT, Angle v to B 15 °
Result: Force = 2.59 × 10⁻⁷ µN
Typical
Given: Charge 10 nC, Velocity 10 m/s, Flux Density 0.5 T, Angle v to B 45 °
Result: Force = 0.03536 µN
High range
Given: Charge 100 nC, Velocity 100 m/s, Flux Density 1.5 T, Angle v to B 75 °
Result: Force = 14.49 µN
Maximum range
Given: Charge 1 µC, Velocity 1 km/s, Flux Density 15 T, Angle v to B 750 °
Result: Force = 7.5 mN
Solving for each variable
Solve for Force
Charge 100 pC, Velocity 10 mm/s, Flux Density 10 G, Angle v to B 1.5 ° → 2.62 × 10⁻¹¹ µN
Solve for Charge
Force 1 mN, Velocity 10 mm/s, Flux Density 10 G, Angle v to B 1.5 ° → 3820 C
Solve for Velocity
Force 1 mN, Charge 100 pC, Flux Density 10 G, Angle v to B 1.5 ° → 3.82 × 10⁸ km/s
Solve for Flux Density
Force 1 mN, Charge 100 pC, Velocity 10 mm/s, Angle v to B 1.5 ° → 3.82 × 10¹⁰ T
How Force changes with Charge
| Charge (input) | Force (result) |
|---|---|
| 1 nC | 0.003536 µN |
| 2.5 nC | 0.008839 µN |
| 5 nC | 0.01768 µN |
| 7.5 nC | 0.02652 µN |
| 10 nC | 0.03536 µN |
| 15 nC | 0.05303 µN |
| 20 nC | 0.07071 µN |
| 40 nC | 0.1414 µN |
| 70 nC | 0.2475 µN |
| 100 nC | 0.3536 µN |
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<p><a href="https://vbatpower.com/formulas/lorentz-magnetic-force/">Lorentz Magnetic Force</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Lorentz Magnetic Force?
Use F = q × v × B × sin(θ). With Charge 10 nC, Velocity 10 m/s, Flux Density 0.5 T, Angle v to B 45 °, Force works out to 0.03536 µN.
What is the formula for Lorentz Magnetic Force?
The formula is F = q × v × B × sin(θ). The magnetic part of the Lorentz force is the force on a charge moving through a magnetic field.
How do you find Charge when you know the other values?
Rearrange for Charge: with Force 1 mN, Velocity 10 mm/s, Flux Density 10 G, Angle v to B 1.5 °, Charge is 3820 C.
How do you find Velocity when you know the other values?
Rearrange for Velocity: with Force 1 mN, Charge 100 pC, Flux Density 10 G, Angle v to B 1.5 °, Velocity is 3.82 × 10⁸ km/s.
Related Concepts
All Fields & Electromagnetism formulas →Need more features?
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