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In the limit of very large conductivity it is convenient to relate the current density J
in the force equation to the magnetic induction B via Ampère's law and to use the
infinite conductivity expression (10.9) to eliminate E from Faraday's law to yield ...
an independent equation, but may be derived by combining the last two
equations in (10.91). Since the force equation in (10.91) is independent of
magnetic field, we suspect that there exist solutions of a purely electrostatic
nature, with B = 0.
Consequently to complete our discussion we must consider the covariant
formulation of the Lorentz force equation and the conservation laws of
momentum and energy. The Lorentz force equation can be written as a force per
unit volume ...
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Introduction to Electrostatics
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