




Physicists conclude that electrostatics can be described by the two conditions:E = 0, E =.
No sources or sinks of Magnetic Field lines; and Ampere's Law.
We can immediately translate the statement that magnetic fields have no sources or sinks into the statement:B = 0, since, (again by the divergence theorem,) we know that sources and sinks correspond to nonvanishing divergence.
You are probably familiar with the BiotSavart Law which describes the magnetic field produced by an electrical current element.
Ampere's Law states that, for constant current flow, the flux of electrical current through a surface is proportional to the line integral of the magnetic field (counterclockwise) around its boundary:
Stokes' Theorem, applied to B, gives
Upon combining these two we obtain, for any surface S:
from which physicists conclude the differential equations of steady state current flow:
B = j / c, B = 0