Particles in Electromagnetic Fields: Ionic and Electronic Optics

Abstract

In general terms, gravitational forces $(\vec P = m\vec g)$ are assumed to be negligible with respect to the forces generated by the fields $\vec E$ and $\vec B$. Respectively, these forces produce a coulombic force as in $q\vec E$ and a Laplace force given by $q\vec v \times \vec B$. Under the action of these forces, a particle of charge q is subject to an acceleration $\vec \gamma = \frac{{\overrightarrow {dv} }} {{dt}}$ which is such that:

$$ \vec F = m\frac{{\overrightarrow {dv} }} {{dt}} = q\vec E + q\vec v \times \vec B = q\left( {\vec E + \vec v \times \vec B} \right).$$

((1))

As detailed in the preceding chapters, the magnetic force is often negligible with respect to the coulombic force.