Abstract
It is known that elementary and nonrelativistic electromagnetic considerations lead to a value for the mass of a spherical electrical distribution that is 4/3 times larger than its value obtained from a relativistic treatment. We have obtained a very simple account of this discrepancy, which makes use only of Coulomb’s law and the Biot–Savart law together with the well-known formulas for the energy densities of the electrostatic and magnetic fields. The resolution of this discrepancy, of course, involves the correct (relativistically covariant) definitions for the momentum and energy of an electromagnetic field. This example shows the necessity for relativistic considerations even in nonrelativistic treatments of electromagnetism.
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