Eur. Phys. J. C (2014) 74: 2838
https://doi.org/10.1140/epjc/s10052-014-2838-y

Regular Article - Theoretical Physics

Magnetic response to applied electrostatic field in external magnetic field

¹ Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, CEP 05508-090 , São Paulo, SP, Brazil
² Department of Physics, University of Florida, 2001 Museum Road, Gainesville, FL, 32611-8440, USA
³ Department of Physics, Tomsk State University, Novoslobodskaja 1, 634050 , Tomsk, Russia
⁴ P. N. Lebedev Physics Institute, 117924 , Moscow, Russia

^* e-mail: tg.adorno@gmail.com
^** e-mail: tadorno@usp.br

Received: 7 March 2014
Accepted: 28 March 2014
Published online: 23 April 2014

Abstract

We show, within QED and other possible nonlinear theories, that a static charge localized in a finite domain of space becomes a magnetic dipole, if it is placed in an external (constant and homogeneous) magnetic field in the vacuum. The magnetic moment is quadratic in the charge, depends on its size and is parallel to the external field, provided the charge distribution is at least cylindrically symmetric. This magneto-electric effect is a nonlinear response of the magnetized vacuum to an applied electrostatic field. Referring to the simple example of a spherically symmetric applied field, the nonlinearly induced current and its magnetic field are found explicitly throughout the space; the pattern of the lines of force is depicted, both inside and outside the charge, which resembles that of a standard solenoid of classical magnetostatics.