Library / Foundations: Physics / FPH-28
Foundations: Physics
Magnetic force on a moving charge
Force on a charged particle moving in a magnetic field.
- Ref
- FPH-28
- Rev
- v1
- Field
- Foundations: Physics
- Result
- F [fN]
θ is the angle between the particle velocity and the field B. Only the perpendicular component contributes. Force is at right angles to both.
A moving charge feels a sideways push in a magnetic field, strongest when the motion is at right angles to the field.
Calculator
- Force in N1.602×10−14 N
- Velocity component across the field2,000,000 m/s
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The force is always sideways, so it bends the path but does no work on the particle.
- The radius of the circular path is r = mv/(qB).
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (fN) | Local step | Change in result |
|---|---|---|---|---|---|---|
| B Field | 0.1 to 5,000 mT | 0.03204 | 1,602 | 1,602 | +10% | +10 % |
| v Speed | 0.01 to 100 10⁶ m/s | 0.0801 | 801 | 800.9 | +10% | +10 % |
| q Charge | 0.1 to 10 10⁻¹⁹ C | 1 | 100 | 99 | +10% | +10 % |
| θ Angle to the field | 10 to 90 ° | 2.782 | 16.02 | 13.24 | +10% | −1.23 % |
Sweep of Field
| Field (mT) | Force (fN) |
|---|---|
| 0.1 | 0.03204 |
| 0.3867 | 0.1239 |
| 1.495 | 0.4791 |
| 5.782 | 1.853 |
| 22.36 | 7.164 |
| 86.47 | 27.7 |
| 334.4 | 107.1 |
| 1,293 | 414.3 |
| 5,000 | 1,602 |
Sweep one variable
Variables and how each one contributes
Force
What the equation gives you. Everything else feeds it.
Charge
Charge of the particle (proton 1.602). Directly proportional.
Speed
Particle speed. Directly proportional.
Field
Magnetic flux density. Directly proportional.
Angle to the field
Angle between velocity and B. Largest at 90°.
Worked example with the values above
- q = 1.602×10−19 C, v = 2,000,000 m/s, B = 0.05 T.
- qvB = 1.602×10−14 N; sin 90° = 1.
- F = 16.02 fN (1 fN = 10⁻¹⁵ N).
Assumptions and limits
- Uniform magnetic field.
- Speed well below light.
Common mistakes
- Using the angle to the field’s normal.
- Forgetting the force direction rule.
Statistics and uncertainty
Magnetic field readings from a probe are good to a few per cent, which transfer directly into the force.
Where it is used
- Particle beam and ion optics.
- Mass spectrometers and tube focusing.
Maths you need
- Magnetic fields: B in tesla
- Sine: perpendicular component