Faraday's paradox

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Brush brush , static magnetic field B, rotation ω, its tangential component v, Lorentz force v × B
When the aluminum disc is turned, a voltage can be picked up on the voltmeter. On the other hand, if you only turn the magnet, the voltage display remains at zero. If you turn the magnet and the aluminum disc equally, a voltage can again be measured.

The Faraday paradox is an experiment, first described by Michael Faraday described, and at first glance to be a contradiction to his law of induction appears.

The experimental arrangement consists of a cylindrical permanent magnet and an adjacent conductive disk , both of which are rotatably arranged on an axis. The axis of symmetry of the magnet and the disk coincide with the axis of rotation, the magnet has its polarization in the axial direction (ie the poles are on the axis). The electrical voltage is measured on the disk between the axle and its edge; for this purpose, sliding contacts are attached to its outside and near the axis.

If the disk is set in rotation while the magnet is at rest, a voltage is created at the terminals. This can be described by the Lorentz force or the flow rule ( unipolar induction ). Terminal tension also occurs when the disc and magnet are mechanically linked and moved together. On the other hand, if only the magnet is moved and the disk is at rest, no terminal tension occurs. This was astonishing for Faraday because he assumed that the only important thing for the creation of tension is that the disk moves against the magnet.

In fact, the magnetic field of the permanent magnet is (largely) independent of its rotation. It therefore makes no difference whether it rotates or not. In contrast , the Lorentz force acts (for a stationary observer) on the electrons in the disk as soon as they are moved in the magnetic field. For this reason, a voltage is measured between the sliding contacts when the disk is rotating.

If the experiment is not viewed from the standpoint of the observer at rest, but as an observer moving together with the disk (rotating around the axis), a voltage of zero will always be measured between the center and the edge of the disk; the magnetic field is independent of any rotation of the magnet. On the other hand, an induction voltage will be detected in the circuit between the sliding contacts rotating (for this observer) because this circuit is a conductor rotating in a magnetic field.

This effect, which is not easy to understand, repeatedly led to misunderstandings and, for example, to various attempts to build a kind of perpetual motion machine , the so-called N-machine , on the basis of unipolar induction .

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