Lorentz Force Calculator

The Lorentz force is calculated using F = q(E + vB·sin α), where q is the particle charge, E is the electric field strength, v is the particle velocity, B is the magnetic field strength, and α is the angle between the velocity and the magnetic field vectors. When there is no electric field, the formula simplifies to F = qvB·sin α. The force is always perpendicular to both the velocity and the magnetic field.

The Lorentz force is the combined electromagnetic force exerted on a charged particle moving through electric and magnetic fields. Named after physicist Hendrik Lorentz, it describes how a magnetic field deflects moving charged particles and how an electric field accelerates them. It is a fundamental principle underpinning devices such as electric motors, particle accelerators, and mass spectrometers.

The direction of the magnetic component of the Lorentz force is given by the right-hand rule: point your fingers in the direction of the particle's velocity, curl them toward the magnetic field direction, and your thumb points in the direction of the force on a positive charge. For negative charges (like electrons), the force is in the opposite direction.

An electron has a charge of −1.6×10⁻¹⁹ C and 0.1c ≈ 2.998×10⁷ m/s. At an angle of 90°, the magnetic force magnitude is F = |q|vB = 1.6×10⁻¹⁹ × 2.998×10⁷ × 0.5 ≈ 2.398×10⁻¹² N (about 2.4 pN). The direction would be opposite to that predicted for a positive charge of the same velocity.

The essential inputs are: particle charge (q) in Coulombs, particle velocity (v) in m/s, magnetic field strength (B) in Tesla, and the angle (α) between the velocity and field vectors. For the full electromagnetic Lorentz force, the electric field strength (E) in N/C (or V/m) is also needed. Setting E to zero computes the purely magnetic component.

The magnetic component of the Lorentz force is zero when: (1) the particle is stationary (v = 0), (2) the particle has no charge (q = 0), (3) there is no magnetic field (B = 0), or (4) the particle moves parallel or anti-parallel to the magnetic field (α = 0° or 180°), since sin(0°) = sin(180°) = 0. The electric force component is zero only if the electric field E = 0 or q = 0.

The Lorentz force is central to many technologies. Electric motors and generators rely on the force between current-carrying conductors and magnetic fields. Particle accelerators and cyclotrons use it to steer charged particles. Mass spectrometers exploit it to separate ions by mass-to-charge ratio. Cathode ray tubes (CRTs), MRI machines, and plasma confinement in fusion reactors all depend on Lorentz force principles.

Yes. Simply enter a negative value for the charge (q), such as −1.6×10⁻¹⁹ C for an electron. The calculator will correctly compute the force magnitude, and the sign of the result indicates the force direction is reversed compared to a positive charge of the same magnitude moving under the same conditions.