振荡磁偶极子的电磁辐射和自转矩
Electromagnetic radiation and the self torque of an oscillating magnetic dipole
摘要：
半径为$R$、质量为$m$、总电荷为$q$的均匀带电球壳，具有围绕固定轴的振荡角速度$Ω(t)$，是磁偶极子的模型，该磁偶极子以固定振荡频率$ω$向其周围的自由空间辐射电磁场。经典电动力学的麦克斯韦-洛伦兹方程的精确解产生作用在球壳上的辐射电阻的自转矩，作为$R$、$q$和$ω$的函数。从壳的牛顿运动方程出发，将其角速度$Ω(t)$与外加力矩联系起来，进而研究磁偶极子对给定时刻的脉冲力矩（例如$t=0$）的响应。偶极子的脉冲响应被发现是因果关系下降到非常小的值$R$（即，作为$R \to 0$），只要在球壳的动态运动方程中使用自转矩的精确表达式。
英文摘要：
A uniformly-charged spherical shell of radius $R$, mass $m$, and total electrical charge $q$, having an oscillatory angular velocity $Ω(t)$ around a fixed axis, is a model for a magnetic dipole that radiates an electromagnetic field into its surrounding free space at a fixed oscillation frequency $ω$. An exact solution of the Maxwell-Lorentz equations of classical electrodynamics yields the self-torque of radiation resistance acting on the spherical shell as a function of $R$, $q$, and $ω$. Invoking the Newtonian equation of motion for the shell, we relate its angular velocity $Ω(t)$ to an externally applied torque, and proceed to examine the response of the magnetic dipole to an impulsive torque applied at a given instant of time, say, $t=0$. The impulse response of the dipole is found to be causal down to extremely small values of $R$ (i.e., as $R \to 0$) so long as the exact expression of the self-torque is used in the dynamical equation of motion of the spherical shell.
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