2.1: Lorentz Force

The Lorentz force is the force experienced by charge in the presence of electric and magnetic fields.

Consider a particle having charge \(q\). The force \({\bf F}_e\) experienced by the particle in the presence of electric field intensity \({\bf E}\) is

\[{\bf F}_e = q{\bf E} \nonumber \]

The force \({\bf F}_m\) experienced by the particle in the presence of magnetic flux density \({\bf B}\) is

\[{\bf F}_m = q{\bf v} \times {\bf B} \nonumber \]

where \({\bf v}\) is the velocity of the particle. The Lorentz force experienced by the particle is simply the sum of these forces; i.e.,

\[\begin{align} {\bf F} &= {\bf F}_e + {\bf F}_m \nonumber \\ &= q\left( {\bf E} + {\bf v} \times {\bf B} \right) \label{m0015_eLF}\end{align} \]

The term “Lorentz force” is simply a concise way to refer to the combined contributions of the electric and magnetic fields.

A common application of the Lorentz force concept is in analysis of the motions of charged particles in electromagnetic fields. The Lorentz force causes charged particles to exhibit distinct rotational (“cyclotron”) and translational (“drift”) motions. This is illustrated in Figures \(\PageIndex{1}\) and \(\PageIndex{2}\).

Additional Reading:

• “Lorentz force” on Wikipedia.

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