Lorentz force

• $\vec{\mathbf{F}}=q(\vec{\mathbf{E}}+\vec{\mathbf{v}}\times \vec{\mathbf{B}})$ is the force (in $\mathrm{N}$) on a particle of charge $q$ moving with velocity $\vec{\mathbf{v}}$ in an electric field $\vec{\mathbf{E}}$ and a magnetic field $\vec{\mathbf{B}}$.
  • $\vec{\mathbf{F}}={\int }_{\mathcal{C}}I(d\vec{\mathbf{\ell }}\times \vec{\mathbf{B}})$ is the magnetic force (in $\mathrm{N}$) on a current-carrying conductor in a magnetic field $\vec{\mathbf{B}}$.
  • $\vec{\mathbf{F}}=I(\vec{\mathbf{\ell }}\times \vec{\mathbf{B}})$ is the magnetic force exerted on a straight wire of length $\ell$ carrying a current $I$ in a uniform magnetic field $B$ where $\theta$ is the angle between $\vec{\mathbf{\ell }}$ and $\vec{\mathbf{B}}$.