Magnetic Flux: Exploring What it Means and Its Units

[ascky]

I started reading Lectures on Electrical Engineering Vol I, Steinmetz. I thought I should be able to understand most of it, but I don't get the first page! It says that: 'The total number of lines of force issuing from a magnet pole is called its magnetic flux. The magnetic flux, phi, of a magnet pole of strength m is, phi = 4*pi*m '.

What does this mean, and what are the units of m? I thought that because the magnetic lines always formed closed circuits that the flux through a closed surface around a magnetic pole should be zero. I'd really appreciate it if someone could explain this to me.

 

[Meir Achuz]

I started reading Lectures on Electrical Engineering Vol I, Steinmetz. I thought I should be able to understand most of it, but I don't get the first page! It says that: 'The total number of lines of force issuing from a magnet pole is called its magnetic flux. The magnetic flux, phi, of a magnet pole of strength m is, phi = 4*pi*m '.

What does this mean, and what are the units of m? I thought that because the magnetic lines always formed closed circuits that the flux through a closed surface around a magnetic pole should be zero. I'd really appreciate it if someone could explain this to me.

If a magnetic pole existed, the equations for a pole of strength m would by much like those for a charge q.
1. "Magnetic flux" here means $$\oint{\bf B\cdot dS}$$.
2. Just like Gauss's law, $$\oint{\bf B\cdot dS}=4\pi m$$,
in Gaussian units.
3. In Gaussian units, the units of m would be gauss-cm^2.
In SI units, I think it would be Webers (Whoever he was).
3. "I thought that because the magnetic lines always formed closed circuits...". That is only in the absence of a magnetic monopole.
With magpoles, magnetostatics becomes just like electrostatics.
I suspect your text is using one end of a long bar magnet as an abstraction for a magnetic pole, and not including the B inside the magnet
in finding the flux of 4\pi m.

 

[vanesch]

Yes, it seems that this book starts off really badly...