Calculatin units for theoretical magnetic point charge

[IAmAZucchini]

Hi,

So, assuming the theoretical existence of a monopole, we would have to alter the maxwell equations to give the magnetic field a divergence, and also to ensure that the divergence of the curl of the electric field is still zero we would have to add a term.

The altered divergence of B would have to be
div(B) = mu0 * ROm

mu 0 being magnetic permeability and ROm being magnetic charge volume density.

I'm having trouble figuring out what the units for the theoretical magnetic point charge, qm, would be - I've figured that the units for the point charge density ROm would be Newtons/(Tesla*meters^2), which doesn't make sense to me - here's how I got it

div(B) => units Tesla/meter
Mu0 has units T/A
so ROm must have units A/m, which equates to Newtons/(Tesla*meters^2)...this doesn't make sense to me because it should be a volume density, not an area density, right?

ALSO, if you try to make an analogy to electric field - E has units of Newtons/Coulomb, and the charge unit is Coulomb - so therefore, if B has units of Tesla, then qm should have units of Newtons/Tesla. Which I guess makes sense, somewhat. HOWEVER, if you do it formally, integrating both sides of the new div(B) equation, you get that the units [qm]=(Newtons*meters)/Tesla.

Yet, with the two results that I did get, the q = ro*V rule is conserved (1/m^2 in ro, *m in q, so m^3 = V is the factor by which they differ)...in short, I've confused myself and don't know what to do.

If someone could point out a mistake in my calculations, or point me in the right direction, I would appreciate it!

Thanks muchly.

 

[eys_physics]

Hi
The unit of $$\mu_{0}$$ shall be
$$[\mu_{0}]=\frac{mT}{A}$$
and therefore the unit for $$\rho_{m}$$ is
$$[\rho_{m}]=\frac{N}{Tm^{3}}$$

Hopefully this will clear up things for you

 

[IAmAZucchini]

Oh, SNAP. Thank you!

What a silly mistake.