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Earnshaw's theorem applies to classical inverse-square law forces (electric and gravitational) and also to the magnetic forces of permanent magnets, if the magnets are hard (the magnets do not vary in strength with external fields).
When a charged particle moves in a static magnetic field, it traces a helical path in which the helix axis is parallel to the magnetic field, and in which the speed of the particle remains constant. Because the magnetic force is always perpendicular to the motion, the magnetic field can do no work on an isolated charge.
Outside of this wire the magnetic induction is zero, in contrast to the vector potential, which essentially depends on the magnetic flux through the cross-section of the wire and does not vanish outside. Since there is no electric field either, the Maxwell tensor F = 0 throughout the space-time region outside the tube, during the experiment ...
This is illustrated in the figure to the right: The work done by the gravitational force on an object depends only on its change in height because the gravitational force is conservative. The work done by a conservative force is equal to the negative of change in potential energy during that process. For a proof, imagine two paths 1 and 2, both ...
Faraday's law is a single equation describing two different phenomena: the motional emf generated by a magnetic force on a moving wire (see the Lorentz force), and the transformer emf generated by an electric force due to a changing magnetic field (described by the Maxwell–Faraday equation).
For zero net magnetic charge density (ρ m = 0), the original form of Gauss's magnetism law is the result. The modified formula for use with the SI is not standard and depends on the choice of defining equation for the magnetic charge and current; in one variation, magnetic charge has units of webers, in another it has units of ampere-meters.
Two new papers shed light on a longstanding mystery in particle physics. Zmeel/E+ via Getty ImagesWhen the results of an experiment don’t match predictions made by the best theory of the day ...
Since the force on charges expressed by the Lorentz equation depends upon the relative motion of the magnetic field (i.e. the laboratory frame) to the conductor where the EMF is located it was speculated that in the case when the magnet rotates with the disk but a voltage still develops, the magnetic field (i.e. the laboratory frame) must ...