- #1
arul_k
- 95
- 1
Apart from the orientation of a compass needle and the pattern formed by iron filings, what other proof do we have of magnetic field lines forming loops?
Incand said:Proofs as in experiments? Otherwise it follows from maxwell's law ##\nabla\cdot \vec B = 0## which there been lots of experiments that verify.
The above means pretty much that at every point there is no "net flow". We can also think of it in terms of magnetic flux:
From that equation it follows by the divergence theorem that the flux through any closed surface is zero ##\oint_S \mathbf B \cdot d\mathbf a = \int_V (\nabla \cdot \mathbf B) \cdot d\tau = 0##. And since as much leave as enter a surface there is no sources or sinks for the magnetic field lines, i.e. no magnetic monopoles where the field lines can "end up" so they must form closed loops.
Perhaps your question was more/less advanced than this, I only had undergraduate EM so perhaps there's more to it that I'm not aware of.
arul_k said:Has there been any experimental proof?
arul_k said:Apart from the orientation of a compass needle and the pattern formed by iron filings, what other proof do we have of magnetic field lines forming loops?
Hornbein said:It is a property of the geometry that produces the magnetic field.
http://physics.weber.edu/schroeder/mrr/MRRtalk.html
I'd like to look at the problem more and give a better answer, but I'm busy now. My best guess is that a charge would have a divergent magnetic field if and only if it were measured from the point of view of a charged particle that was moving at the speed of light relative to it. Charged particles have mass, so that can't happen.
The main thing to know is that the magnetic force on a charged particle is perpendicular both to the magnetic field vector and to the velocity vector of the charged particle. The force is never in the direction of the magnetic field vector, like you might expect.arul_k said:Thanks for all the replies. I went thru the link posted by Hornbien and I quote a line from that link:
In summary, we can account for the direction of the magnetic force on the test charge no matter which way it's moving, and this motivates us to introduce a magnetic field vector that points into the page, with the force given by a cross-product of v and B
There dosen't seem to be any reason stated for assuming that the magnetic field vector should point into the page as stated above, so why has this assumption been made.
arul_k said:There dosen't seem to be any reason stated for assuming that the magnetic field vector should point into the page as stated above, so why has this assumption been made.
Yes. The failure to detect magnetic monopoles in all experiments designed to detect them.arul_k said:Has there been any experimental proof?
This is incorrect. Experiments designed to detect magnetic monopoles assume that Maxwells equations are violated. They then measure the amount of that violation. So far that has always been 0, and if it is ever not 0 it will be huge news and a likely Nobel prize.arul_k said:These equations are derived based on the observation / assumption that magnetic field lines form closed loops and therefore the equations cannot be used as proof of the same.
Magnetic field lines are an abstract concept used to represent the direction and strength of a magnetic field. They are imaginary lines that show the path a test magnetic north pole would take in the presence of a magnetic field.
Magnetic field lines form loops because they always form closed curves. This is due to the fact that magnetic field lines always have both a north and south pole, and these poles attract or repel each other, causing the lines to form loops.
Magnetic field lines never cross because it would require the existence of a magnetic monopole, which has never been observed. A magnetic monopole is a single pole, either north or south, without its opposite. Since all magnets have both a north and south pole, the field lines cannot cross.
The density of magnetic field lines represents the strength of a magnetic field. The closer the lines are together, the stronger the magnetic field. Conversely, the farther apart the lines are, the weaker the magnetic field.
No, magnetic field lines cannot be seen with the naked eye. They are an abstract concept used to visualize the direction and strength of a magnetic field. However, they can be observed indirectly using iron filings or a compass to trace the lines around a magnet.