Magnetic Force

#Physics

$\displaystyle \vec{F}=\int \vec{v}\times \vec{B} , \mathrm{d}q=\int \vec{I}\times \vec{B} , \mathrm{d}\ell'=\int \vec{K}\times \vec{B} , \mathrm{d}a'=\int \vec{J}\times \vec{B} , \mathrm{d}\tau'$

• $\displaystyle \vec{v}$ is the velocity of the charge
• $\displaystyle \vec{I}=\lambda \vec{v}$ and is the current
• $\displaystyle \vec{K}=\sigma \vec{v}$ and is the surface current density
• $\displaystyle \vec{J}=\rho \vec{v}$ and is the current density