We consider a linear magnetic response to a point electric charge embedded in the background of parallel constant electric and magnetic fields in the framework of nonlinear electrodynamics. We find two types of responses. One is given by a vector potential free of any string singularity. The corresponding magnetic field may be thought of as two magnetic poles of opposite polarity coexisting at one point. The other response is given by a vector potential singular on a half-axis directed along the background fields. Its magnetic field is a magnetic monopole plus a field confined to an infinitely thin solenoid, whose role is the same as that of the Dirac string. The value of the magnetic charge is determined by the electric charge and the background fields and is expressed in terms of derivatives of the nonlinear local Lagrangian. Once the potential is singular, the nonlinear Maxwell equations written for potentials and field intensities are not equivalent. We argue why the preference should be given to potentials.

中文翻译：

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恒定场背景中嵌入的点状电荷产生的磁极

在非线性电动力学的框架内，我们考虑对嵌入恒定平行电场和磁场背景中的点电荷的线性磁响应。我们发现两种类型的响应。一个由没有任何字符串奇异性的向量电势给定。相应的磁场可以被认为是在一个点上共存的两个相反极性的磁极。另一个响应由沿背景场指向的半轴上的矢量电位奇异值给出。它的磁场是一个磁单极子，外加一个局限于无限薄螺线管的磁场，其作用与狄拉克弦相同。电荷的值由电荷和背景场确定，并以非线性局部拉格朗日导数表示。一旦电势是奇异的，为电势和场强编写的非线性麦克斯韦方程就不等价。我们争论了为什么应该优先考虑潜力。