We study a simple system of charges and currents, consisting of two electric dipoles that are driven by exponentially growing currents running between the ends of each dipole. The exponential time dependence allows the electric and magnetic fields to be calculated exactly. The forces between the dipoles must be evaluated carefully when the exponential growth is slow and are shown to not be equal and opposite. The imbalance is accounted for by the rate of change of momentum in the electromagnetic field, so that the total momentum is conserved even though Newton's third law fails. Implications for momentum conservation for “semistatic” slowly varying currents, for which the Biot–Savart law is applicable, are discussed.
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2021
Author(s)
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