- #1
Heimdall
- 42
- 0
Hi,
I'm stuck with a question concerning electric fields : Can an electrostatic potential drop exist in (what I would call) a 0 dimensional system ?
Let's imagine we are in a region of space where there is nothing but a uniform magnetic field. So the problem is anisotropic but does not depend on the position. We then decide to move in a certain direction (not aligned to the magnetic field).
When we have reached a constant velocity, say V, we see, in our reference frame, a magnetic field B', almost identical to B, and an electric field which has a value given my the lorentz transformation E'=-VxB.
V and B being uniform and constant over time, E is uniform and also constant in our reference frame.
I wondered what was the "source" of the electric field seen in the moving frame. As it is a constant, it cannot be a induction field. It therefore has to be an electrostatic field. Ok but then were is the source ?
I was stuck for a while with this question when I realized that I forgot the current density consistent with the static magnetic field in initial frame. In the moving frame, a part of this current density *must* be seen as a charge density that would thus be consistent with the electrostatic field.
Ok but then, if there's an electrostatic field, where is the potential drop ? My problem does not depend on any variable, the magnetic field is uniform in all space(*), saying this must be somehow the same as saying that the gradient of the electrostatic potential is zero ? But I see an electric field... This electric field can be very strong (depends on B and V) but we continue to ignore variations (derivatives) ... this looks like a paradox to me.
(*) maybe the solution lies in the assumption of uniformity ? I mean assuming the magnetic field is completely uniform must be somehow wrong, but don't exactly see what's going on...
Thanks for your help !
Heim.
I'm stuck with a question concerning electric fields : Can an electrostatic potential drop exist in (what I would call) a 0 dimensional system ?
Let's imagine we are in a region of space where there is nothing but a uniform magnetic field. So the problem is anisotropic but does not depend on the position. We then decide to move in a certain direction (not aligned to the magnetic field).
When we have reached a constant velocity, say V, we see, in our reference frame, a magnetic field B', almost identical to B, and an electric field which has a value given my the lorentz transformation E'=-VxB.
V and B being uniform and constant over time, E is uniform and also constant in our reference frame.
I wondered what was the "source" of the electric field seen in the moving frame. As it is a constant, it cannot be a induction field. It therefore has to be an electrostatic field. Ok but then were is the source ?
I was stuck for a while with this question when I realized that I forgot the current density consistent with the static magnetic field in initial frame. In the moving frame, a part of this current density *must* be seen as a charge density that would thus be consistent with the electrostatic field.
Ok but then, if there's an electrostatic field, where is the potential drop ? My problem does not depend on any variable, the magnetic field is uniform in all space(*), saying this must be somehow the same as saying that the gradient of the electrostatic potential is zero ? But I see an electric field... This electric field can be very strong (depends on B and V) but we continue to ignore variations (derivatives) ... this looks like a paradox to me.
(*) maybe the solution lies in the assumption of uniformity ? I mean assuming the magnetic field is completely uniform must be somehow wrong, but don't exactly see what's going on...
Thanks for your help !
Heim.