📂Electrodynamics

Magnetism and the Law of Lorentz Force

Definition¹

A moving charge (current) creates a magnetic field $\mathbf{B}$ around it. The force experienced by a charge $Q$ moving at velocity $\mathbf{v}$ in a magnetic field $\mathbf{B}$ is given by:

$$ \begin{equation} \mathbf{F}_{m}=Q(\mathbf{v} \times \mathbf{B}) \end{equation} $$

This force is called the magnetic force, and the above formula is known as the Lorentz force law.

Explanation

As with the definition of an electric field, when a moving charge experiences a force like $(1)$ surrounding a current, we call $\mathbf{B}$ the magnetic field produced by the current.

It is said that the Lorentz force law was actually discovered by Oliver Heaviside. When there is an electric field, the general formula, including the electric force due to Coulomb’s law, is as follows:

$$ \mathbf{F}=Q\left[ \mathbf{E} + (\mathbf{v}\times\mathbf{B}) \right] $$

This is a fundamental axiom of electromagnetic theory and an experimental law.