The Zero in Maxwell's Equations

Maxwell's Equations (Home)


There is one zero that is present in Maxwell's Equations, which shows up in Gauss' Magnetic Law. As you know, zero means the absence of something - that which does not exist. And this particular zero means that magnetic monopoles do not exist.

In Gauss' Law for Electric Fields, we see that the divergence of the Electric Flux Density is equal to the volume electric charge density. However, when we take the divergence of the magnetic flux density, the result is not equal to the volume magnetic charge density.


Since the discovery of Maxwell's Equations and modern physics, physicists have been trying to find the magnetic monopole. A finding would make Maxwell's Equations much more symmetric. If electric charge exists and gives rise to Electric Fields, and Magnetic Fields also exist, why do magnetic charges (monopoles) not exist?

No one has a good explanation, and to this day physicists are looking for them. But this zero, this all-important zero, is a declaration that they have not been found. Magnetic dipoles do exists (as in magnets with a north and south pole), but no matter how many times you break a magnetic dipole it will never form two monopoles - you'll just get smaller magnetic dipoles.

Magnetic charge is measured in Webers. This equation has the units of Webers/meter^3 (magnetic charge density), so this zero is measured has units of [Wb/m^3].

there are no magnetic monopoles
[Equation 1]

Maxwell's Equations

This page on the non-existance of magnetic monopoles is copyrighted; no portion should be copied without the author's permission. Copyright, 2012.