Asymmetries in Maxwell’s Electrodynamics W. J. Wilson Department of Engineering & Physics University of Central Oklahoma Edmond, OK 73034 Web: www.physics.uco.edu/wwilson Email: wwilson@uco.edu

ON THE ELECTRODYNAMICS OF MOVING BODIES By A. EINSTEIN “It is known that Maxwell's electrodynamics - as usually understood at the present time - when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighborhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighborhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise - assuming equality of relative motion in the two cases discussed - to electric currents of the same path and intensity as those produced by the electric forces in the former case.” Engineering & Physics

Motionless Magnet/Galvanometer When there is no relative motion, there is no current indicated by the galvanometer: B = Const.        ∂B/∂t = 0      E = 0. Engineering & Physics

Moving Magnet Moving bar magnet generates time change of magnetic field. Variable magnetic field, in turn, generates induced electric field according to the Maxwell's equation: inside the coil that moves free electrons of the coil producing induced current through the galvanometer, whose needle is moving left and right. Engineering & Physics

Moving Coil When bar magnet stands still, there is no time variation of magnetic field and there is no induced electric field, according to Maxwell's equations: B = Const.        ∂B/∂t = 0       E = 0 However, the galvanometer needle is equally moving left and right. This phenomenon is now explained by the Lorentz's force: F = q v x B that acts on free electrons of the coil. This is obviously inconsistent being that the two last cases are equivalent and they should be described by same fundamental equations. Engineering & Physics

Maxwell Electrodynamics Hertz Electrodynamics Scientists were aware of this asymmetry of Maxwell's equations at the beginning of the 20th century. Hertz proposed a variant of Maxwell's equations (H.R. Hertz, Electric Waves), that differed slightly from Maxwell's original form (partial derivatives were substituted by total ones), and that did not "lead to asymmetries" as mentioned by Einstein and are invariant to Galilean transformations. Maxwell Electrodynamics Hertz Electrodynamics Engineering & Physics

Moving Frames Let's now append a truck to the previous experiment. Let's take into consideration that part of the case when bar magnet SN moves toward the coil, say by the velocity v1 = 3m/s. For the blue observer O1 on the illustration, the galvanometer needle turns due to induced electric field that pushes electrons in the coil. Let's now take that this observer with all his gadgets is inside a truck that moves by the opposite velocity v2 = -v1 = -3m/s. For another observer O2 outside the truck, the bar magnet is standing still, while the coil is moving toward the bar. For that observer, there is no electric field and the galvanometer needle turns due to Lorentz force. In other words, the same physical event is described by two different equations, i.e. by two different physical laws. Namely, in the first case by the low of electromagnetic induction, and in the second case by the low of Lorentz force. Thus, it is violated one of the fundamental postulate of physics: The laws of physics are the same in all inertial frames! Engineering & Physics

Moving Truck and Special Relativity Using Special Relativity, we'll start with green observer O2, since E2 = 0 in the coil for him Now get the electric field in the coil inside the reference frame of the blue observer O1. Applying relativity transformations on E2, we get: E1 = E2 +  v2×B/c, Since: E2 = 0, we get, finally: E1 = v2×B/c. Engineering & Physics

From these results we can deduce the conclusions Expressions for relativistic transformation of electric and magnetic field: E1 = E2* +  v2×B/c, B1 = B2* −  v2×E/c, it may be seen that they comprise just those parts missing from Maxwell's equations that are included in Hertzian equations: If the bar magnet moved by a non-uniform velocity, it would be inappropriate to use special relativity for it is valid just for uniform transformations. Engineering & Physics

Faraday Homopolar Generator Asymmetry Faraday noticed that only the rotation of the copper disk above the magnet influences the generated potential. The rotation of the permanent magnet does not affect the magnitude of generated potential at all! Copper Disk Permanent Magnet Engineering & Physics

Action-Reaction Asymmetry v1 1 R 2 v2 Engineering & Physics

References H.R. Hertz, Electric Waves: Being researches on the Propagation of Electric Action with Finite Velocity through Space, Cornell University Press (1893) ISBN: 1429740361 Petrovic Branko, “Lorentz's Force”, http://www.angelfire.com/sc3/elmag/files/MaxLor.html H. Aspden, “Electromagnetic Reaction Paradox” , Lettere Al Nuovo Cimento 39, 247 (1984). Engineering & Physics

References H.R. Hertz, Electric Waves: Being researches on the Propagation of Electric Action with Finite Velocity through Space, Cornell University Press (1893) ISBN: 1429740361 Petrovic Branko, “Lorentz's Force”, http://www.angelfire.com/sc3/elmag/files/MaxLor.html H. Aspden, “Electromagnetic Reaction Paradox” , Lettere Al Nuovo Cimento 39, 247 (1984). Engineering & Physics