Question

Magnetic force on a charged particle, moving in a magnetic field is given by

Answer 1

Magnetic field $\vec{B}$ acts on a particle with a charge $q$ moving with a velocity $\vec{v}$ with a force given by Lorentz law :

$\vec{F}=q [\vec{v}\times\vec{B}]$ , where I note $[\vec{a}\times\vec{b}]$ - vector product of $\vec{a},\vec{b}$ .

However in general case we need to consider both magnetic and electrical force on a particle, as these two fields are closely tied on to the other. This expression is called 'generalized Lorentz law' :

$\vec{F}=q [\vec{v}\times\vec{B}]+q\vec{E}$