Electromagnetic Force (Lorentz) Calculator

The Lorentz force is the total electromagnetic force acting on a charged particle moving through electric and magnetic fields — a foundational concept in physics and electrical engineering. Enter the particle's charge (q), velocity (v), electric field strength (E), magnetic field strength (B), and the angle between v and B into the Electromagnetic Force (Lorentz) Calculator to get the Total Lorentz Force, broken down into its electric force component and magnetic force component. Also try the calculate Dipole Moment (p), Dipole Moment in Debye & Polarity Assessment — Dipole Moment.

C

Electric charge of the particle in Coulombs

m/s

Speed of the charged particle

N/C

Strength of the electric field

T

Strength of the magnetic field in Tesla

°

Angle between velocity vector and magnetic field

Results

Total Lorentz Force

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Electric Force Component

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Magnetic Force Component

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Frequently Asked Questions

How do I calculate the Lorentz force?

The Lorentz force is calculated using F = q(E + v×B), where q is the charge, E is the electric field strength, v is the velocity, and B is the magnetic field strength. The magnetic component also depends on the angle between velocity and magnetic field vectors. See also our Magnetic Field of Straight Wire Calculator.

What is the Lorentz force on an electron moving in a 0.5 T magnetic field?

For an electron (charge = -1.6×10⁻¹⁹ C) moving perpendicular to a 0.5 T magnetic field, the force depends on its velocity. At 10⁶ m/s, the magnetic force would be approximately 8×10⁻¹⁴ N perpendicular to both velocity and field directions.

How do I find the direction of the deflection due to the Lorentz force?

The magnetic component of Lorentz force is always perpendicular to both the velocity vector and magnetic field vector. Use the right-hand rule for positive charges: point fingers in velocity direction, curl toward magnetic field, thumb points in force direction. For negative charges, the force is opposite.

What are the key inputs required for Lorentz force calculation?

You need five key parameters: particle charge (q), particle velocity (v), electric field strength (E), magnetic field strength (B), and the angle between velocity and magnetic field vectors. The calculator can solve for any missing parameter if the others are provided. You might also find our Skin Depth Calculator useful.

What are common applications of Lorentz force?

Lorentz force is fundamental in many devices including electric motors, particle accelerators, mass spectrometers, cathode ray tubes, and magnetic levitation systems. It's also crucial in understanding plasma physics and the behavior of charged particles in space.

Why is the angle between velocity and magnetic field important?

The magnetic component of Lorentz force depends on sin(α), where α is the angle between velocity and magnetic field. Maximum force occurs at 90° (perpendicular), while no magnetic force acts when the particle moves parallel to the field (0° or 180°).

How accurate are Lorentz force calculators?

Lorentz force calculators are highly accurate for classical physics applications. They use the fundamental electromagnetic equations and provide precise results within the limits of classical mechanics. For relativistic speeds (near light speed), relativistic corrections may be needed.