What is the magnetic equivalent to the Coulomb?

[fagricipni]

For electric charges the relation is $F=k\frac{q_1q_2}{r^2}$, where $k=\frac{1}{4\pi\varepsilon_0}$. It seems to me that for the (hypothesized) magnetic monopole one could write an equivalent $F=n\frac{p_1p_2}{r^2}$. I have replaced the q's with p's for "pole strength", and k with n -- no mnemonic there, just picked a letter. In both equations F is a force measured in newtons and r is a distance measured in meters. In the SI base units the q's are measured in ampere-seconds, and k is a function of $\varepsilon_0$. What should the p's be measured in in SI base units, and does $n=\frac{1}{4\pi\mu_0}$?

 

[phyzguy]

Since there is no evidence magnetic monopoles exist, there is no defined unit for their magnetic charge.

 

[Vanadium 50]

There is something called the Biot-Savart Law that is similar to Coloumb's Law.

I strongly, strongly, strongly recommend that you NOT start from thius point. It will clarify nothing and reinforce your misconceptions.

 

[osilmag]

For electric charges the relation is $F=k\frac{q_1q_2}{r^2}$, where $k=\frac{1}{4\pi\varepsilon_0}$. It seems to me that for the (hypothesized) magnetic monopole one could write an equivalent $F=n\frac{p_1p_2}{r^2}$. I have replaced the q's with p's for "pole strength", and k with n -- no mnemonic there, just picked a letter. In both equations F is a force measured in newtons and r is a distance measured in meters. In the SI base units the q's are measured in ampere-seconds, and k is a function of $\varepsilon_0$. What should the p's be measured in in SI base units, and does $n=\frac{1}{4\pi\mu_0}$?

Magnetic forces arise from current not from static charges.

 

[DaveE]

Here's my short, very hand-wavy, description of why this idea doesn't work:
- Electric charges (monopoles) exist, and can be easily observed. They can create an E-field from a single point in space.
- Magnetic charges (monopoles) have never been observed, in spite of lots of effort. Maybe they will be seen someday in extremely unusual places/situations, IDK. But they certainly don't effect your life today.
- Magnetic fields are created from moving electrons, which by that very nature is many points in space. The current that creates B-fields moves from somewhere to somewhere else. This means that you will have to add up the contributions to the B-field over space (the current path, sort of).

Maxwell did a nice job of explaining classical EM. This is where you're answers lie.
In particular: $\nabla \cdot \vec E = \frac {\rho}{\epsilon_o}$ and $\nabla \cdot \vec B = 0$
It's going to be really hard to identify or attach units to something that is always, under all circumstances zero.

 

[fagricipni]

First, I am aware that magnetic monopoles are only theorized particles. I've been thinking about how to describe what I am doing, and I'm thinking that there should be a kind of symmetry between electric and magnetic behavior. The mention of the Biot-Savart Law actually relates to one symmetry that I am trying to explore: A beam of electric monopoles; e.g., electrons from an electron gun, creates a magnetic field which encircles the beam; likewise, a beam of magnetic monopoles should create an electric field that encircles the beam. Electric current is measured in amperes which are coulombs per second, so a magnetic current should be measurable in some unit per second, where that unit is the magnetic equivalent of the coulomb. It seems to me that the all of behaviors described for electric charges would have their analogs for magnetic charges if such magnetic charges exist. Certainly, the magnetic field outside of a magnetic dipole looks the same an the electric field outside of an electric dipole.

 

[renormalize]

It seems to me that the all of behaviors described for electric charges would have their analogs for magnetic charges if such magnetic charges exist.

This is all well-trodden ground. From https://en.wikipedia.org/wiki/Magnetic_monopole:

Note that in 1931 Dirac proved that if monopoles exist, both the fundamental electric charge $q_e$ and magnetic charge $q_m$ must be quantized such that their (suitably normalized) product is an integer:

And using these formulae, or indeed the generalized Maxwell equations above them, it's easy to show that, depending on your choice of convention, magnetic charge carries units of webers or ampere-meters: