Surface Current Density

Current per unit width on a surface

$\vec{K}\equiv \frac{\mathrm{d}\vec{I}}{\mathrm{d}{l}_{\perp }}$

• $\mathrm{d}\vec{I}$ is the current on a surface
• $\mathrm{d}{l}_{\perp }$ corresponds to the length of wire perpendicular to the current
  

$\vec{K}=\sigma \vec{v}$

• $\sigma$ is the surface charge density
• $\vec{v}$ is the velocity of the charge density