Unipolar induction

Unipolar induction means the separation of electrical charges by means of the magnetic part of the Lorentz force and the associated creation of an electric voltage. Although use may be generated by unipolar induction both DC voltages and AC voltages, the main application in the production of direct voltages. A typical arrangement consists of an electrically conductive circular disk that rotates in a magnetic field parallel to the axis ( Unipolarmaschine ).

• 2.1 Calculation taking into account the Lorentz force
• 2.2 Calculation of the flow control

Unipolar induction in a conductor loop

Description

A particularly simple arrangement, occurs in the unipolar induction, shows the opposite arrangement. The conductor rod moves with the speed in a temporally and spatially constant magnetic field with the flux density. The ends of the conductor bar are connected to metal rails, at the end of the drawn -voltage can be measured.

For the following description it is assumed that the observer is in the laboratory frame in which to rest the metal rails:

The conductor bar, due to the magnetic component of the Lorentz force, a force acts on the electrons ( the electron charge, q = -e), the " down " indicates a result of the negative charge of the electrons. The Lorentz force that allows the closing of the circuit, an electrical current can flow.

In the illustrated open conductor circuit, however, no electric current flow in the steady state. Thus, the Lorentz force can not be the only force acting on the electrons. The observer in the laboratory system concludes therefore that in the moving metallic conductor in addition to the Lorentz force, a Coulomb force must be present in the "up" shows in the conductor bar and compensates the Lorentz force. The Coulomb force he explained by a previous charge separation of the electrons.

In a closed resistive conductor circuit is obtained after a certain time is always a balance between the Lorentz force and Coulomb force (i.e., there is no acceleration of the electrons held in the steady state ), and it is observed a positive terminal voltage.

If there is an electric vortex field?

In the following, the obvious question is designed to ascertain whether the measured voltage on the voltmeter is caused by vortex fields with closed electric field lines.

The law of induction

Describes how the rate of change of magnetic flux density caused electric eddy fields. Because the magnetic flux density for the described arrangement is constant in time, is considered in the present case

Consequently, there are no electrical eddy fields in the uniform motion of the conductor bar.

Although the current reasoning is accurate and computationally easy to verify, it still seems to lead at first glance to be an insurmountable contradiction, which can be described as follows:

The apparent contradiction can be resolved by using the special theory of relativity. The main misconception that leads to the apparent contradiction is that the metallic ( conductive assumed to be ideal ) conductor bar is free of electric fields. In fact, the electric field strength is basically dependent on the reference frame in which it is measured. Metal conductors can only be accepted in such frames of reference than approximately field-free, in reality, resting from their perspective of the ladder. Transforming the electric field strength in the moving conductor bar using the Lorentz transformation in the quoted without line rest frame ( laboratory system ), it can be seen that the static observer measures a nonzero electric field in the conductor bar that was made plausible in the introductory statement of the Lorentz force. The conductor bar includes the view of the laboratory system therefore, an electric field which compensates for the ( also measured in the laboratory ) voltage.

Unipolar induction in the Faradayscheibe

Calculation taking into account the Lorentz force

To generate a DC voltage, the linear arrangement with the moving conductor bar is not suitable, since the conductor bar with the time ever would move away from the terminals. Instead, a cylindrically symmetrical arrangement offers similar to how the Faradayscheibe shown on the left.

The terminal voltage at the Faradayscheibe based - like in the example with the moving conductor rod - on the Lorentz force on the carrier in the rotating body. It is assumed that the disc at an angular velocity around its axis rotates in a homogeneous magnetic field parallel to the axis. In this case, a voltage between the axis and a sliding contact at a distance from the axis is measured.

The Lorentz force

On the conduction electrons, which rotate with the disc, is in balance with the force in the field generated by the charge separation electric field

• : Vector of the magnetic flux density
• : Velocity vector
• : Elementary charge.

Since perpendicular to is when the magnetic field penetrates the disk vertically, the force equilibrium holds, ie.

• : Distance of the electron from the axis of rotation
• : Angular velocity of the disk
• : Field strength of the Lorentz force corresponding electric field.

By integration of e (R) results in the induced voltage between the central axis and the edge of the disc with radius R:

It is clear that the voltage occurring can not be explained using the second Maxwell's equation. Because no matter at which place the ( stationary ) observer with his meter might go: It measures once he has taken his rest, always a constant magnetic flux density with! Thus, there are, in his view no vortices of the electric field, which is equivalent to saying that there is no induction.

Calculation using the flow control

With the flow control without the derivation of integral calculus is done:

Here, the angle ( radian ) of the circular sector of the area A, which is penetrated by the magnetic field. d / dt is the time derivative symbolized. The sign in is omitted, the polarity results from the three- finger rule.

Producing alternating voltages

The particular advantage of an approach based on unipolar induction generator is that you can produce a DC voltage without the use of a rectifier. Nevertheless, it is also possible using the unipolar induction, to produce alternating voltages. In the case of moving on rails conductor bar you can for example move the conductor bar periodically around a mean back and forth or in the case of Faradayscheibe drive these with varying degrees of circulation so that the disc rotates times in one direction and sometimes in the other direction.

Law of induction and unipolar induction

In case of incorrect application of the law of induction can occur in the framework of classical electrodynamics problem of understanding about the causes of unipolar induction. This fact is expressed in the Faraday paradox or the paradox of herring and is partly contributed by the historical concept formation. Essential for the correct application of the law of induction is that the imaginary line that is to be determined along which the circulation induced voltage, and the ruling on their electric field are observed in each case from the same reference system is out. The correct application of the law of induction is in the context of relativistic electrodynamics, a subfield of special relativity theory, possible and requires the use of the Lorentz transformation.