Tuval’s Electromagnetic Spaceship
نویسندگان
چکیده
1 Problem In two recent e-prints, Tuval and Yahalom proposed " electromagnetic spaceships " based on the net force exerted on a pair of time-dependent current loops [1], or a time dependent current loop and a permanent magnet [2]. Show that rocket propulsion (net gain of mechanical momentum of an isolated system) is possible in the first example, but not in the second. Ampère argued [3] that the static forces on a pair of steady electrical currents are equal and opposite. He had no concept of electromagnetic (field) momentum. Maxwell (sec. 57 of [5]) interpreted Faraday's electrotonic state as the vector potential A, and gave an interpretation of this as " electromagnetic momentum, " in the sense that P (Maxwell) EM = ρA (C) c dVol (1) is electromagnetic momentum associated with an electric charge density ρ in the (Coulomb-gauge) vector potential (in Gaussian units, with c being the speed of light in vacuum). Maxwell also argued (sec. 792 of [6]) that the radiation pressure P of light 2 is equal to its energy density u, P = u = D 2 4π = H 2 4π (2) for an electromagnetic wave with fields D and H in vacuum, but he did not explicitly associate this pressure with momentum in the electromagnetic field. 1 Ampère also had no concept of electromagnetic fields, which were first discussed by Faraday, sec. 2147 of [4]. 2 Apparently, Kepler considered the pointing of comets' tails away from the Sun as evidence for radiation pressure of light [7].
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