What Does v Represent in the Lorentz Force Equation?

[kmarinas86]

The "v" of the Lorentz Force

If I have a rotating magnetic dipole that is rotating at an accelerated rate, then it is clear that the "v" of the "B" increases around the axis of that dipole's rotation. In addition, this should affect the "v" of the "q" affected by the "B", but the force induced on that q exists at a right angle. Isn't "v" of the Lorentz Force much different though? Is this "v" really the relative velocity of source charge of the magnetic field and the charge being affected (i.e. in that it does not rotate with the "B" field)? If this were not the case, then "v" could easily exceed the speed of light, which makes no sense of course. If instead, the former were the case, then different source charges would have different contributing B's as well as different contributing v's. But if those v's have absolutely nothing to do with B-field lines cutting through charges at "v", then at this stage should we reject the notion of B-field lines cutting charges at "v". If we should, how should we look at it then? What is "v" when distance from source of the magnetism * angular velocity of magnetic dipole > c? Can the velocity addition formula be used here, and how (if applicable)?

 

[Bill_K]

If I have a rotating magnetic dipole that is rotating at an accelerated rate, then it is clear that the "v" of the "B" increases around the axis of that dipole's rotation... ..."v" could easily exceed the speed of light, which makes no sense of course.

kmarinas86, An interesting thing about electromagnetic fields is that they do not move. They always sit still. There is no such thing as the "velocity v of a B field", because the field of a moving object is equivalent to a set of E and B fields at rest. If you run past a charge, or run past a magnet, what do you see? Answer: not a moving E or B field, rather time varying E and B fields. The fields you see in your comoving frame are given by the Lorentz transform of the original field.

The example of the rotating magnet adds more interest, since as you point out the apparent velocity increases as you get farther away and eventually exceeds c. What is really happening? A rotating magnet is a time-varying magnetic dipole, and therefore it radiates. In fact the energy that it radiates requires that a constant torque be applied at the axis to keep it moving. More importantly, at large distances the electromagnetic field changes character. As one gets farther away, the E and B fields being produced gradually turn into an outgoing electromagnetic wave.

 

[kmarinas86]

kmarinas86, An interesting thing about electromagnetic fields is that they do not move. They always sit still. There is no such thing as the "velocity v of a B field", because the field of a moving object is equivalent to a set of E and B fields at rest. If you run past a charge, or run past a magnet, what do you see? Answer: not a moving E or B field, rather time varying E and B fields. The fields you see in your comoving frame are given by the Lorentz transform of the original field.

The example of the rotating magnet adds more interest, since as you point out the apparent velocity increases as you get farther away and eventually exceeds c. What is really happening? A rotating magnet is a time-varying magnetic dipole, and therefore it radiates. In fact the energy that it radiates requires that a constant torque be applied at the axis to keep it moving. More importantly, at large distances the electromagnetic field changes character. As one gets farther away, the E and B fields being produced gradually turn into an outgoing electromagnetic wave.

Then is the "v" of the Lorentz Force the "v" of the relative velocity between a charge in the magnet and the charge outside the magnet being affected?

If that is the case, doesn't this make it inaccurate to calculate "v" relative to a charge and "B" relative to an observer? "v" and "B" are supposed to be calculated relative to the same inertial frame, correct?

 

[Bill_K]

Just pick an inertial frame and calculate everything with respect to that frame, the B field, the E field (there will likely be one) and the force on the charge.