Question

Suppose we are leaving in a two dimensional world (i:e: there is no z direction/axis).
Assuming that Gauss’s law is valid in this world, find the electric field at a distance
r from for a point charge q. Is the answer same as what we studied in class?

Answer 1

Answer

Gauss law in 2D would have to be:

$\oint E. \hat{n} dl= 2\pi Q$

because you are reducing in 3D to a line in 2D, and keep the idea of measure of the boundary and its orthogonal direction or normal. Therefore some data are changed.