The electrostatic force ( F_1 ) and magnetic force ( F_2 ) acting on a charge q moving with velocity v can be written:

$\displaystyle \overrightarrow{\mathrm{F}}_1=\mathrm{q} \overrightarrow{\mathrm{E}}, \overrightarrow{\mathrm{~F}}_2=\mathrm{q}(\overrightarrow{\mathrm{~B}} \times \overrightarrow{\mathrm{V}})$

$\displaystyle \vec{F}_1=q \vec{E}, \vec{F}_2=q(\vec{V} \times \vec{B})$

$\displaystyle \vec{F}_1=q \vec{B}, \vec{F}_2=q(\vec{B} \times \vec{V})$

$\displaystyle \overrightarrow{\mathrm{F}}_1=\mathrm{q} \overrightarrow{\mathrm{~V}} \cdot \overrightarrow{\mathrm{E}}, \overrightarrow{\mathrm{~F}_2}=\mathrm{q}(\overrightarrow{\mathrm{~B}} \cdot \overrightarrow{\mathrm{~V}})$