Lorentz Force Calculator

Lorentz Force on a Charged Particle

A charged particle in electric and magnetic fields experiences the Lorentz force. This calculator uses a simplified one-dimensional form where the velocity is perpendicular to the magnetic field, so the magnetic contribution is $qvB$.

Formula

$$F = qE + qvB$$

Here $q$ is charge in coulombs, $E$ is electric field in N/C, $v$ is velocity in m/s, and $B$ is magnetic field in tesla. The electric term $qE$ acts along the field; the magnetic term $qvB$ is perpendicular to both velocity and field in the full vector form.

Applications

Lorentz force appears in cyclotrons, mass spectrometers, electric motors, and particle physics experiments. For an electron at $0.1c$ in a $0.5\,\text{T}$ field, the magnetic force is on the order of $10^{-12}\,\text{N}$.

Frequently Asked Questions

What is the full Lorentz force equation?

The vector form is $\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$. This tool uses the 1D simplification with $\sin\theta = 1$ for the magnetic part.

When is the magnetic force zero?

When velocity is zero, the magnetic field is zero, or the velocity is parallel to the magnetic field so $\sin\theta = 0$.

What charge should I use for an electron?

The elementary charge is $1.602 \times 10^{-19}\,\text{C}$. Use a negative value for electrons if you want the force direction to reflect negative charge.

How do I find velocity from speed of light?

Multiply the fraction of $c$ by $2.998 \times 10^8\,\text{m/s}$. For example, $0.1c \approx 3.0 \times 10^7\,\text{m/s}$.

Can electric and magnetic forces cancel?

Yes, if $qE = -qvB$ the net Lorentz force is zero. This is the principle behind velocity selectors in particle beam instruments.

Report

Lorentz Force on a Charged Particle

Formula

Applications

Frequently Asked Questions

Related Tools

Recent Visits