在均勻電場之下之介電質圓錐之電場行為

Abstract

當在處理介電材質時，塊材往往容易因為表面不平滑而產生尖點。在模擬實驗中發現這種尖點能夠產生發散電場。為了研究這件事情，我們引進了在介電材質圓錐底下時的格林函數並套用到均勻帶電板試圖去模擬外加均勻電場。在解釋發散電場時，我們必須考慮到極化電荷間的競爭關係。由於電磁波和聲波的數學公式相同，相信這個研究也能對於聲學產生幫助。

While dealing with the dielectric, it is usually to see the sharp tip for the non-smooth surface of the material. Numerical experiment shows that the singularity of field will be generated. To investigate, we introduce the Green function for the dielectric cone and apply to the uniformly charged slab to simulate the constant external electric field. To account for the singularity, the competition between polarized charges is needed to consider. Also, owing to the same mathematical structure for electromagnetic waves and sound waves, it may do a favor to the acoustics.