Key Equations

Force on a charge in a magnetic field	$\vec{F} = q \vec{v} \times \vec{B}$
Magnitude of magnetic force	$F = q v B sin θ$
Radius of a particle’s path in a magnetic field	$r = \frac{m v}{q B}$
Period of a particle’s motion in a magnetic field	$T = \frac{2 π m}{q B}$
Force on a current-carrying wire in a uniform magnetic field	$\vec{F} = I \vec{l} \times \vec{B}$
Magnetic dipole moment	$\vec{μ} = N I A \hat{n}$
Torque on a current loop	$\vec{τ} = \vec{μ} \times \vec{B}$
Energy of a magnetic dipole	$U = − \vec{μ} \cdot \vec{B}$
Drift velocity in crossed electric and magnetic fields	$v_{d} = \frac{E}{B}$
Hall potential	$V = \frac{I B l}{n e A}$
Hall potential in terms of drift velocity	$V = B l v_{d}$
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	$v_{max} = \frac{q B R}{m}$