electric flux density

The electric field remains unchanged and the electric flux density increases by a factor Er.

This is a difficult boundary-value problem, but using the method of images we only need to determine the electric flux density due to the two point charges.

If the electric flux density does not change very fast, the second term on the right hand side (the displacement flux) is very small and can be left out, and then the equation is the same as Ampere's law.