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Simplier is more difficult



On Wed, 8 Oct 1997, David Bowman wrote that "a uniform pure B field" can
not be viewed as a relativistic manifestation of an electric field.

At the risk as exposing my limitations (and hoping to learn more from being
criticized) let me desagree with David's argument. I will ignore "intrinsic
magnetic moments" of elementary particles, mentioned by James, and argue on
the basis of what I recall after a casual reading of an article more than
ten years ago. Here it is:

1) Consider a point charge at rest. Its simple field E has no effect on
a magnetic probe (a small bar magnet or a current loop) situated nearby.
Move it with some speed v and the probe responds. We say B is a new
field due to motion and we define it mathematically in terms of F, q
and v.

2) But motion is relative. I can place myself in a frame of reference in
which the value of v is zero. In that frame B=0. This is true for any
v, even when v<<c. From my frame of reference the undeniable effect
response of the probe must be described in terms of E only. I take it
for granted (?) that this is always possible when a charge q moves
along a short segment of its trajectory.

3) An electric current in a wire (a collective motion of electrons) sets
a macroscopic magnetic field B around it. That B can be calculated at
any point by integration of contributions made by each wire element.

B=Integral(dB)

where dB is given by the Biot Savart formula.

4) But dB is a magnetic field created by a moving charge in a short wire
segment dL. If each dB is a relativistic representation of an electric
field then the same must be true for B. Thus a magnetic field of any
electric circuit can be viewed as a superposition of many relativistic
manifestations of electric fields.

This kind of thinking applies to any set of electric circuits, including
a large solenoid imagined by David to produce a uniform magnetic field in
a finite region of space.
Ludwik Kowalski