Mansuripur’s Paradox
نویسندگان
چکیده
An electrically neutral current-loop, with magnetic dipole m0, that is at rest in a static, uniform electric field E0 experiences no force or torque. However, if that system is observed in the lab frame where the loop has velocity v parallel to E0, and v c, where c is the speed of light, then there appears to be an electric dipole moment, p = v/c×m0 associated with the loop (in Gaussian units). Näıvely, the torque on this moment due to the electric field (which has strength E = E0 +O(v2/c2) in the lab frame) is τ = p× E ≈ E0vm0/c. Can/should the torque be different in different frames of reference? The paradox is compounded by supposing the static, “uniform” electric field is due to a single electric charge q at large, fixed distance from the magnetic moment in the rest frame of the latter, and the lab-frame velocity v is along the line of centers of the charge and moment. Discuss the force on charge q in the lab frame. This paradox was first posed by Spavieri [2] and more recently by Mansuripur [6]. It is a conceptual variant of a famous problem by Shockley [12] that introduced the concept of “hidden mechanical momentum.”
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