Normal Derivative

$\frac{\partial V}{\partial n}=\nabla V\cdot \hat{n}$

$\sigma =-{\epsilon }_0\frac{\partial V}{\partial n}$

• Surface charge

${\partial }_n{V}_{+}{|}_{x=0}-{\partial }_n{V}_{-}{|}_{x=0}=-\frac{\sigma }{{\epsilon }_0}$

• ${\partial }_n{V}_{+}$ is the normal derivative of the voltage just above a surface
• $\sigma$ is the surface charge density
• ${\epsilon }_0$ is the permitivity of free space