Key Equations

Force on a charge in a magnetic field	$\overrightarrow{F}=q\overrightarrow{v}\times \overrightarrow{B}$
Magnitude of magnetic force	$F=qvB\text{sin}\theta$
Radius of a particle’s path in a magnetic field	$r=\frac{mv}{qB}$
Period of a particle’s motion in a magnetic field	$T=\frac{2\pi m}{qB}$
Force on a current-carrying wire in a uniform magnetic field	$\overrightarrow{F}=I\overrightarrow{l}\times \overrightarrow{B}$
Magnetic dipole moment	$\overrightarrow{\mu }=NIA\widehat{n}$
Torque on a current loop	$\overrightarrow{\tau }=\overrightarrow{\mu }\times \overrightarrow{B}$
Energy of a magnetic dipole	$U=\text{−}\overrightarrow{\mu }·\overrightarrow{B}$
Drift velocity in crossed electric and magnetic fields	$v_d=\frac{E}{B}$
Hall potential	$V=\frac{IBl}{neA}$
Hall potential in terms of drift velocity	$V=Bl{v}_d$
Charge-to-mass ratio in a mass spectrometer	$\frac{q}{m}=\frac{E}{B{B}_{0}R}$
Maximum speed of a particle in a cyclotron	$v_{\text{max}}=\frac{qBR}{m}$