⚡ Lorentz Force Calculator
Calculate force on charged particles in electric and magnetic fields
Use scientific notation (e.g., 1.6e-19 for electron charge)
Leave 0 if only magnetic field is present
Required for magnetic force calculation
Leave 0 if only electric field is present
90° for perpendicular (maximum magnetic force)
How to Use This Calculator
Enter Charge
Input the electric charge of the particle in Coulombs. Use scientific notation for elementary particles (e.g., 1.6e-19 for electron, -1.6e-19 for proton).
Enter Electric and/or Magnetic Fields
Input the electric field strength (N/C or V/m) and/or magnetic field strength (Tesla). You can calculate with either field alone or both together. Leave the other as 0 if not applicable.
Enter Velocity and Angle (for magnetic field)
If calculating magnetic force, input the particle's velocity in m/s and the angle between velocity and magnetic field vectors in degrees. Use 90° for perpendicular (maximum force).
Calculate
Click the "Calculate Lorentz Force" button to get the total force in Newtons. The calculator shows both electric and magnetic force components separately.
Formula
F = q(E + v × B)
Where:
- F = Lorentz Force (Newtons, N)
- q = Charge (Coulombs, C)
- E = Electric Field (Newtons per Coulomb, N/C or Volts per meter, V/m)
- v = Velocity (meters per second, m/s)
- B = Magnetic Field (Tesla, T)
- θ = Angle between velocity and magnetic field vectors (degrees)
Component Forces:
Felectric = qE
Fmagnetic = q(v × B) = qvB sin(θ)
Example Calculation:
For an electron (q = -1.6×10⁻¹⁹ C) with v = 1×10⁶ m/s, B = 0.1 T, θ = 90°:
F = (-1.6×10⁻¹⁹) × (1×10⁶) × 0.1 × sin(90°)
F = -1.6×10⁻¹⁴ N
Note: The magnetic force is perpendicular to both velocity and magnetic field. The electric force is parallel to the electric field. Negative force indicates opposite direction for negative charges.
About Lorentz Force Calculator
The Lorentz Force Calculator determines the total force acting on a charged particle moving in both electric and magnetic fields. The Lorentz force combines the electric force (F = qE) and magnetic force (F = q(v × B)) into a single expression. This fundamental equation explains how charged particles move in electromagnetic fields and is essential in particle physics, plasma physics, and electrical engineering.
When to Use This Calculator
- Particle Physics: Analyze motion of charged particles in accelerators and detectors
- Plasma Physics: Understand charged particle behavior in plasmas
- Electromagnetic Fields: Calculate forces in combined electric and magnetic fields
- Physics Education: Solve problems involving charged particle motion
- Engineering: Design systems involving charged particle beams
Why Use Our Calculator?
- ✅ Combined Fields: Handles both electric and magnetic forces together
- ✅ Quick Calculation: Instantly determine force from field values
- ✅ Scientific Notation: Handles very small charge values (elementary particles)
- ✅ Free Tool: No registration or payment required
- ✅ Educational: Learn about electromagnetic forces and particle motion
Common Applications
Particle Accelerators: Calculate forces on charged particles in cyclotrons, synchrotrons, and linear accelerators. The magnetic force causes particles to move in circular paths, while electric fields accelerate them. Understanding Lorentz force is essential for designing and operating particle accelerators used in research and medical applications.
Cathode Ray Tubes and Displays: Determine electron deflection in CRT displays and oscilloscopes. Electric fields deflect electrons vertically, while magnetic fields can deflect them horizontally. The Lorentz force explains how electron beams are controlled to create images on screens.
Mass Spectrometers: Analyze how charged particles are separated by mass-to-charge ratio using magnetic fields. The Lorentz force causes particles to move in circular paths with radius proportional to momentum, allowing identification of different particle masses.
Tips for Best Results
- Magnetic force is zero when velocity is parallel to magnetic field (θ = 0°)
- Magnetic force is maximum when velocity is perpendicular to field (θ = 90°)
- Magnetic force does no work (perpendicular to velocity), only changes direction
- Electric force can do work and change particle energy
- For negative charges, force directions are reversed
Frequently Asked Questions
What is the Lorentz force?
The Lorentz force is the total force acting on a charged particle in electromagnetic fields: F = q(E + v × B). It combines the electric force (qE) and magnetic force (q(v × B)) into one equation. This fundamental force explains how charged particles move in electric and magnetic fields.
Why is the magnetic force perpendicular to velocity?
The magnetic force is given by the cross product F = q(v × B), which by definition is perpendicular to both v and B. This means magnetic fields can change the direction of motion but cannot change speed (they do no work). Only electric fields can change particle energy.
What happens when velocity is parallel to magnetic field?
When velocity is parallel to magnetic field (θ = 0°), sin(0°) = 0, so magnetic force is zero. The particle continues in a straight line unaffected by the magnetic field. Only when velocity has a component perpendicular to B does magnetic force act.
Can the Lorentz force change particle energy?
The electric component can change energy (since F·v ≠ 0), but the magnetic component cannot (since (v × B)·v = 0). Magnetic fields only change direction, causing circular or helical motion. Electric fields can accelerate or decelerate particles.
How does charge sign affect the force?
Negative charges experience forces opposite to positive charges. In electric fields, negative charges move opposite to field direction. In magnetic fields, the direction of circular motion reverses. The magnitude remains the same, but direction depends on charge sign.
What is the right-hand rule for magnetic force?
For positive charges: point fingers in direction of velocity, curl toward magnetic field direction, thumb points in force direction. For negative charges, force is opposite. Alternatively: F = q(v × B) gives force direction (perpendicular to both v and B).