时变电场不能产生磁场的实例

A Example of no Magnetic Field in a Time Varying Electric Field

设真空中一点电荷q位于O点,q随时间t成正弦变化,q=q_0sinωt, 它周围的电场呈球体状向周围扩散,构成一区域Ω,其中各点的电场强度E都随时间变化,从动态标量位函数φ的波动方程出发可算出该区域内磁场为零。但运用麦克斯韦第一方程式计算将得出Ω内有磁场存在的错误的结果。其原因在于麦克斯韦第一方程式的积分式中同一时刻L环路所张的曲面S可以有无穷多张,该积分式要求L环路所张的的所有曲面S_n上对δD/δ_t的积分值应相同。但是某些特殊情况下,例如本例就不满足这一点。麦克斯韦第一方程式的微分式所算出的“H”矢量在某些特殊情况下,例如本例仅仅是代表一种数学意义上的存在而非物理意义上的磁场强度H矢量存在。在真空中,如时变电场方向呈均匀球状均匀分布,则该电场所在的区域不产生磁场,麦克斯韦第一方程式在此区域内不成立。

Presumed a point charge q at the O point in the vacuum and q takes place sinusoidal change with time t, q =q_0 sin ωt. The electric field preduced by q like a spread of a ball in the field all over, it forms a area Ω, the electric intensi-ty E of every point in it changes with t. Passing some calculations from wave equation of dynamic scalar quantity function φ,a result of no magnetic field in Ω can get. However, it whould obtain a wrong result of used Maxwell 's 1st equation in the ex-ample. The reason is there are infinite curved surfaces in the L circle in Maxwell's 1st equation's integral equation at thesame time, the integral equation demands the integral figures of D/t are same on the all curved surfaces, but some special cas-es such as this example don' t demand this point. To obtain a'H' vector used Maxwell's 1st equation's differential equation, it only represents a mathemaics' existence but not a true existence of magnetic intensity 'H'. To sum up ahove, in vacuumif the direction of time varying electric field is well distributed and like a ball there is no magnetic field in it, maxwell's 1st e-quation cannot be used in the erea.