| Earnshaw's Theorem |
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Information AboutEarnshaw's Theorem |
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This follows from Gauss's Law . The force acting on an object F(''x'') (as a function of position) due to a combination of inverse-square law forces (forces deriving from a potential which satisfies Laplace's Equation ) will always be divergenceless (·F = 0) in free space. What this means is there is no point in empty space where the force due to the field points inward from all directions. Since such a point is the only place where a stationary charge could be stable, any arrangement of such charges is unstable and will tend to collapse. There are no local Minima or Maxima of the field potential in free space, only Saddle Point s. This theorem also states that there is no possible static configuration of Ferromagnet s which can stably Levitate an object against gravity, even when the magnetic forces are stronger than the gravitational forces. There are, however, several exceptions to the rule's assumptions which allow Magnetic Levitation . Earnshaw’s Theorem, in addition to the fact that configurations of classical charged particles orbiting one another are also unstable due to electromagnetic radiation, pointed the way to quantum mechanical explanations of the structure of the atom. REFERENCES
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