Re: [Phys-l] Magnetic force and work

[John Denker <jsd@av8n.com>]

Rauber, Joel wrote:

> In cases where the magnetic field is time-dependent:
>
> dB/dt != 0
>
> Is the magnetic force doing mechanical work?  Or is it an electric force
> produced by the induced electric field that is doing work?  (I.e. the
> non-conservative component of the electric field)

Yes/no.

> (preferably elaborate on any yes/no answer)

It depends on your reference frame.

Actually from a spacetime viewpoint there's almost no distinction
between E and B.

By way of analogy, in three dimensions momentum is a 3-vector, and is
invariant w.r.t rotations as a vector should be.  In spacetime, the
4-momentum is a 4-vector, and is invariant w.r.t spacetime rotations
(including boosts) as it should be.  The three spacelike components
of this 4-vector do not have the full set of invariances.

By the same token, in spacetime there is really only one critter, F.
In any given observer's reference frame we can decompose F into an E piece
and a B piece, but another observer may decompose it differently.

  Actually, the invariant gorm of F is equal to B^2 - E^2, so all
  observers agree on whether the field is "mostly" magnetic or "mostly"
  electric, but that is not very helpful to the present discussion.
  We have a mostly magnetic field which does/doesn't have a small but
  important electric component.

Suppose we have a magnet that is moving relative to the lab frame.
For simplicity, let's restrict attention to the low-frequency limit
where we can neglect radiation.

If you are comoving with the magnet, you will say that the field F
is purely magnetic.  If you are sitting in the lab frame, you will
say that this same field F has an electric component.