IAmAZucchini
Mar23-08, 04:29 PM
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.
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.