Lorentz Force Calculator
Free calculate force on charged particle in electric and magnetic fields using f = q(e + v×b). Get instant, accurate results with our easy-to-use calculator.
Input Parameters
e = 1.602×10⁻¹⁹ C (electron charge)
Set to 0 if only magnetic field present
Set to 0 if particle is stationary
Set to 0 if only electric field present
90° = perpendicular, 0° = parallel
Results
Enter parameters to calculate
What is the Lorentz Force?
The Lorentz force is the force experienced by a charged particle moving through both electric and magnetic fields. It combines the electric force (qE) and the magnetic force (qv×B) into a single expression.
The electric force acts in the direction of the electric field and depends only on the charge and field strength. The magnetic force is perpendicular to both velocity and magnetic field, and only acts on moving charges.
The Lorentz force is fundamental in understanding particle accelerators, mass spectrometers, cathode ray tubes, and many other devices that manipulate charged particles using electromagnetic fields.
Lorentz Force Formula
Where:
- • F = Lorentz force (N)
- • q = Charge (C)
- • E = Electric field (V/m)
- • v = Velocity (m/s)
- • B = Magnetic field (T)
- • × = Cross product
Components:
F_electric = qE (parallel to E)
F_magnetic = q(v × B) = qvB sin(θ) (perpendicular to v and B)
How to Calculate
-
1
Convert all units to SI
Charge to Coulombs, velocity to m/s, magnetic field to Tesla, angle to radians if needed.
-
2
Calculate electric force
F_e = qE (scalar multiplication, direction same as E).
-
3
Calculate magnetic force
F_m = qvB sin(θ) where θ is angle between v and B. Direction: perpendicular to both v and B (right-hand rule).
-
4
Add forces vectorially
F_total = F_electric + F_magnetic (vector addition).
Practical Examples
Example 1: Electron in Magnetic Field
Electron (q = -1.602×10⁻¹⁹ C) at 10⁶ m/s, B = 0.1 T, perpendicular (θ = 90°).
Solution:
F_m = qvB sin(90°) = 1.602×10⁻¹⁹ × 10⁶ × 0.1 × 1
F_m = 1.602×10⁻¹⁴ N (perpendicular to motion)
Example 2: Combined Fields
Charge: 1 μC, E = 1000 V/m, v = 500 m/s, B = 0.05 T, θ = 90°.
Solution:
F_e = 1×10⁻⁶ × 1000 = 0.001 N
F_m = 1×10⁻⁶ × 500 × 0.05 = 2.5×10⁻⁵ N
F_total ≈ 0.001 N (electric force dominates)
Applications
Particle Accelerators
Guiding and accelerating charged particles using magnetic fields in cyclotrons, synchrotrons, and linear accelerators.
Mass Spectrometers
Separating ions by mass-to-charge ratio using magnetic deflection, essential in analytical chemistry and physics.
Electron Devices
Cathode ray tubes, electron microscopes, and displays using electric and magnetic fields to control electron beams.
Education
Teaching electromagnetism, understanding charged particle motion, and demonstrating electromagnetic principles.
Frequently Asked Questions
What is the right-hand rule for magnetic force?
Point fingers in direction of velocity, curl toward magnetic field. Thumb points in direction of force on positive charge. For negative charge, reverse direction.
Why doesn't magnetic field do work?
Magnetic force is always perpendicular to velocity (F_m ⟂ v), so F_m · v = 0. Work = F·d, and since force is perpendicular to motion, no work is done. Magnetic fields change direction, not speed.
What happens when v is parallel to B?
When θ = 0° (parallel), sin(0°) = 0, so F_m = 0. The particle moves in a straight line along the field lines. Only electric field affects it.
Can electric and magnetic forces cancel?
Yes! If E and v×B are opposite and equal magnitude, forces cancel. This is the principle behind velocity selectors: F_e = -F_m when v = E/B.
What is the motion in uniform B field?
Perpendicular to B: circular motion (radius r = mv/(qB)). Parallel to B: straight line. Combined: helical motion (spiral along field lines).