Lorentz Force Calculator
An electron at 10⁶ m/s crossing a 0.5 T field feels a force of 8.01088 × 10⁻¹⁴ N, bending it into a circle about 11 µm in radius.
8.01088317 × 10⁻¹⁴ N
- Radius of the circular path mv⊥/(|q|B)
- 0.00001137126021 m
- Cyclotron frequency |q|B/(2πm)
- 13996244940 Hz
- Acceleration F/m
- 8.794100054 × 10¹⁶ m/s²
Step-by-step solution
- F = |q| v B sin θ = (1.602176634 × 10⁻¹⁹) × 1000000 × 0.5 × sin 90°
- F = 8.01088317 × 10⁻¹⁴ N
Lorentz Force Formula
F = q v B sin θ, F = B I L sin θ
orbit radius r = mv⊥/(|q|B); cyclotron frequency f = |q|B/(2πm)
Worked Example
An electron moving at 10⁶ m/s at right angles to a 0.5 T field:
- F = |q| v B sin θ = (1.602176634 × 10⁻¹⁹) × 1000000 × 0.5 × sin 90°
- F = 8.01088317 × 10⁻¹⁴ N
Cyclotron frequency |q|B/(2πm): 13996244940 Hz · Acceleration F/m: 8.794100054 × 10¹⁶ m/s²
GATE tip
The force between two parallel wires is F/L = μ₀I₁I₂/(2πd), attractive for currents in the same direction. It once defined the ampere: 2 × 10⁻⁷ N/m for 1 A at 1 m.
More Electromagnetic Fields Calculators
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Magnetic Field Calculator
B = μ₀I/(2πr) (wire), μ₀NI/(2R) (loop centre), μ₀μᵣNI/l (solenoid)
toroid B = μ₀μᵣNI/(2πR); H = B/(μ₀μᵣ)
Example: A long straight wire carrying 10 A, at 1 cm: Magnetic flux density B = 0.2 mT.
-
Capacitance Calculator
C = ε₀εᵣA/d
coax C = 2πε L/ln(b/a); concentric spheres 4πε ab/(b − a); isolated sphere 4πε a
Example: Two 100 cm² plates 1 mm apart in air: Capacitance C = 88.5419 pF.
-
Inductance Calculator
L = μ₀μᵣN²A / l
toroid: l = 2πR (mean radius); coax: L/length = (μ₀/2π) ln(b/a)
Example: A 200-turn air-cored solenoid, 20 mm in diameter and 100 mm long: Inductance L = 157.914 µH.
-
Electric Field Calculator
E = q/(4πε r²), λ/(2πε r), σ/(2ε)
ε = ε₀εᵣ; potential of a point charge V = q/(4πε r)
Example: A 1 nC point charge, 1 m away, in air: Electric field |E| = 8.98755 V/m.
Frequently asked questions
Does the magnetic force do work?
No: it is always perpendicular to the velocity, so it changes direction but not speed. Electric fields do the work in particle accelerators.
How do I find the direction?
Use the right-hand rule for positive charges (F = qv × B) and reverse it for electrons.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Lorentz Force Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/lorentz-force-calculator/
IEEE
Scientific Converters, "Lorentz Force Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/lorentz-force-calculator/