According to the special relativity, charge (= ρe ) and electric current (= J ) are NOT constant values. But the moment observer starts to move, "positive" charges are generated (= Fig.1 right, S' ) ! This unrealistic transformation is indispensable for special relativity to agree with Maxwell equation. As shown on this site (p.12-15), Maxwell equations can keep their form under Lorentz transformation, if upper equation hold.
So special relativity must agree with Maxwell equation with respect to the constant light speed "c". But, the moment the observer moves, the strange positive charges are generated inside electric wire. In Fig.5 left (= S ), the observer at rest is looking at neutral wire in which electric current J is flowing. But while the observer is moving in x direction, the positive charge is moving in the opposite direction from obesrver's viewpoint (= S' ).
This means this charge experiences Lorentz magnetic force, and turns toward wire ONLY in S' frame. To solve this problem, new charges must be generated, and their electric force cancels magnetc force, as shown on this site. When a charged particle is moving at velocity "v in the presence of magnetic field B, it experiences the magnetic force ( F = evB ). The direction of this magnetic force is perpendicular both to the velocity and the magnetic field. If this observer starts to move (= S' ), the charged particle is moving in the opposite direction from the observer's viewpoint. As a result, in S' frame, this charge experiences Lorentz magnetic force from current, and is accelerated toward the wire ! Because this charge is at rest in S frame, but moves toward the wire ONLY in S' frame, as shown in Fig.10. This means if Lorentz magnetic law and special relativity is right, the observer has supernatural power to control the particle's motion without touching it ! To avoid paradoxical situation of Fig.10, this neutral electric wire has to produce new positive charges only in S' frame, as shown in Fig.11 right ! If the wire gets positive, new electric field (= E ) can cancel magnetic force ( eE = evB in Fig.12 right ).
But if a charged particle (= negative ) is at the position of Fig.13, this particle is attracted toward the wire ONLY in S' frame. Because the electric force acting on this particle cannot be cancelled out by magnetic force. So depending on the observer's movement, it is determined whether this charged particle is accelerated or not toward the wire. When the observer is moving in x direction, the wire and particle move in minus x direction. So this magnetic force (= evB ) is NOT in the x direction, it cannot cancel the electric force (= eE ) in x direction. As a result, this charged particle is at rest in S, but is accelerated toward the wire in S', which means "paradox".
According to Biot-Savart law, this electric current cannot generate the magtetic field in the x direction. In the upper section, we explain the reason why fatal paradox occurs with respect to charge and current.
If the charge and current transformation is contradictory, the relation of electromagnetic fields should also break down, too. In Fig.16 left (= S ), electric fields in all directions are zero, only magnetic field B exists. If the neutral wire changes into positive one, it means some negative charges are removed from the wire !
It is unbelievable that the observer can remove these negative charge without touching them. But if this idea is true, this observer has "supernatural" power to teleport charges ONLY by their momevent.


According to the four-current of special relstivity, minus charges of the upper wire teleport to the lower wire just by simple observer's movement !
Because the stronger repulsive force among electrons in the lower wire does NOT allow this teleportation.
As you feel, it is natural that electrically neutral wire remains neutral irrespective of the observer's movement. To do so, we have to correct the wrong idea that Lorentz force depends on the observer's velocity, as shown in Fig.8,9. If the observer has nothing to do with Lorentz force law, there must be other factors to determine whether magnetic force is generated or not. Like this, when the chaged particle is moving relative to the earth (ether), it causes de Broglie waves, and magnetic field around it. In this case, fatal paradoxes of Lorentz force do NOT happen, and the observer doesn't need to have "unnatural" power.
The standard relativity explains these strange phenomena from the perspective of the distance between charges, as shown on this site and this site.
When the observer is moving at speed "v" in x direction (= S' ), negative charges appear stationary, and instead, positive charges are moving in -x direction in S' frame.
According to Lorentz contraction, in Fig.24 left, negative charges are moving, so the spacing between adjacent negative charges is reduced.
As this wire is neutral, the distances between negative and positive changes are the same. In S frame, the rest length between positve charges is l0, and its charge density is ρ+.
In S' frame, the distance between them is Lorentz-contracted, which means charge density increases, as shown in Fig.25 right. On the other hand, the distance between negative charges is originally Lorentz- contracted in S frame.
When the observer starts to move at the same velocity as these negative charges (= S' ), their distances are expanded (= return to their rest length ). So in S' frame, the length of this wire becomes Lorentz-contracted ( l → l' ), because it is moving in S'. According to special relativity, charge density (= ρ ) and current density (= J ) transform like spacetime (= t, x, y, z ) under Lorentz transformation. If the z component of the particle's velocity is zero in S frame, it must remain zero also in S' frame. So, the new generated electric force must be just cancelled by magnetic force in z direction. As a result, both in S and S' frames, the net forces in z direction acting on the particle become zero. According to the quantum electrodynamics (QED), electron charge (e-) does not change under Lorentz transformation. Actually, the constant charge "e" is used in the fine structure constant and magnetic moment in QED. Here we explain this invariance from the viewpoint of classical electromagnetism and special relativity. Because even if the length "l" is contracted, the charge density ρ is increased and cancel each other.
Also in S frame, two charges (= 2 × q ) enter the box during dt, which means 2q is increased in the box during dt. So in all reference frame, the relation between charge density ρe and current density J must be satisfied. The change of electric currents (= J ) in all x, y, z directions causes the change of the charge density (= ρ ) in this box. The relation of Eq.4 among charge density and current must hold in all reference frames, when total charge is conserved. If you believe in the special relativity, the time (= ct ) and space (= x, y, z ) coodinate need to change as four-vector under Lorentz transformation. And in any inertial reference frame, the relationship between charge and current density must be satisfied, as shown in Fig.38. To satisfy Eq.7, the charge and current density must change as four-vector like time and space coordinate, which causes "strange" phenomenon as I explained above.


In the classical mechanics, the strange transformation of the time, space and charge do NOT happen.
As a result, in any frames of classical mechanics, the normal relation between charge and current is satisfied. In Eq.15, the position of ( x', y', z' ) are specified somewhere in S' frame and independent from the time t'. To make the relationship of Eq.7 Lorentz invariant, the charge and current densities need to transform like ( ct, x, y, z ). As a result, the special relativity needs the Lorentz transformation of Eq.18 in the electromagntetism. If you look for Lorentz transformation of electric and magnetic fields in some websites or something, you will find the transformations of Eq.23. The important point is that electric field in the moving direction (= Ex ) does NOT change under Lorentz transformation (= blue line ), though new charges are generated inside wire.
In electromagnetism, electric and magnetic potentials are expressed using electric (= scalar ) and magnetic (= vector ) potentials. Of course, as shown on this page, these potentials are artificially introduced only for unifying relativity and electromagnetism. For Maxwell's equation to satisfy special relativity, these A and φ must obey the following relations under Lorentz transformation.
In S frame (= rest frame ) in Eq.26, the current J is constant, and it generates constant (= static ) magnetic field B. The important point is that current J in the upper wire cannot generate magnetic field at the position of the external negative charge due to the Biot-Savart relation (= outer product ) of Eq.28. The electric and magnetic fields are expressed using vector and scalar potentials, as shown in Eq.27. According to the Biot-Savart law, the magnetic field B can be expressed using the current J.
As shown in Eq.28, the magnetic field becomes zero at the position in the direction of current J due to the outer product. So at the position of the negative charge in Eq.26, the magnetic field B from the upper wire always becomes zero. These new generated charges inside wire can cause electric field only in the z and y direction ( but not x direction !
As you see, relativistic electromagnetism ( Lorentz force ) is effective only in the directions perpendicular to the electric current J.
But the magnetic field ( from the upper wire ) at the external charge is zero, due to Biot-Savart law of Eq.28. Even if some magnetic fields are generated, when this external charge moves very slowly, it can come closer to the electric wire only in S' frame, in which new strange charges are created. Consists of two metal rings connected by an aluminum beam that can rotate freely on a support.
This kit is designed for elementary through high school students to learn the principles and applications of electromagnets. Polarity of voltage on deflecting plates and polarity of electromagnet can both be reverted.
The First Aid Kit includes new rubber mats for your controller, as well as replacement thumbsticks with potentiometers.
Includes two coils on plastic spools a U shape iron core, a straight iron core, two magnetic needles with stands, and a pair of wires. As the torch is shaken the magnet inside passes through a copper coil producing electricity. Made of four layers of 0.67 mm wires (23 gauge) with approximately 710 turns of polyurethane enameled copper wire. All coils are wrapped with 20 gauge magnet wire with insulated binding posts as connectors. This includes the mechanism for the thumbsticks plus the potentiometers that work with the mechanism.



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