Electric and magnetic fields in RS
Posted: Thu Dec 11, 2014 9:35 am
Dear all,
I am a bit confused from the electric and magnetic charges and fields as used in RS, so I would appreciate if someone could help me by understanding it. My confusion results from the following:
In the book Structure of the physical universe Larson introduces the concept of magnetic charge and magnetic potential M. The magnetic potential he uses is probably different from magnetic vector potential commonly denoted as A. He explicitly mentions that the gradient of the magnetic potential is the magnetic field intensity (chapter XXIX). Later he makes it clear that that by magnetic field intensity (which is unfortunately in english a bit confusing because of it's usage for two distinct fields - in terms of mathematical fields) he termed magnetic induction commonly denoted as B. However
∇×B = j+dD/dt
Which is often a non-zero expression. From this would follow that ∇×(∇M) is not equal 0 - that is mathematically impossible...
Further more (and more importantly) he explicitly shows the dimensions of the electric charge q as t.s-1 and the dimensions of the magnetic flux φ as t2.s-2. However the product of the two qφ should have the dimensions of action [coulomb× weber]=[joule×seconds] which in reciprocal system is t2.s-1 whereas if we multiply their dimensions we get the dimensions of mass t-3s-3.
If you can clarify this please go into detail as much as you can.
Thank you very much.
Jan
I am a bit confused from the electric and magnetic charges and fields as used in RS, so I would appreciate if someone could help me by understanding it. My confusion results from the following:
In the book Structure of the physical universe Larson introduces the concept of magnetic charge and magnetic potential M. The magnetic potential he uses is probably different from magnetic vector potential commonly denoted as A. He explicitly mentions that the gradient of the magnetic potential is the magnetic field intensity (chapter XXIX). Later he makes it clear that that by magnetic field intensity (which is unfortunately in english a bit confusing because of it's usage for two distinct fields - in terms of mathematical fields) he termed magnetic induction commonly denoted as B. However
∇×B = j+dD/dt
Which is often a non-zero expression. From this would follow that ∇×(∇M) is not equal 0 - that is mathematically impossible...
Further more (and more importantly) he explicitly shows the dimensions of the electric charge q as t.s-1 and the dimensions of the magnetic flux φ as t2.s-2. However the product of the two qφ should have the dimensions of action [coulomb× weber]=[joule×seconds] which in reciprocal system is t2.s-1 whereas if we multiply their dimensions we get the dimensions of mass t-3s-3.
If you can clarify this please go into detail as much as you can.
Thank you very much.
Jan