论文标题
角依赖性表面电极的静电场
Electrostatic Field of Angular-Dependent Surface Electrodes
论文作者
论文摘要
我们提出了一种分析策略，以找到具有角度依赖电位的表面电极SE产生的电场。该系统是一个平面区域$ \ MATHCAL {A} $，保存在固定但不均匀的电势V（ϕ）$的情况下，具有任意的角度依赖性。我们表明，生成的电场是由于两个磁场的贡献：一个依赖于平面区域轮廓上的循环 - 在类似于生物范围的（bsl）项中 - 以及另一个涉及$ \ Mathcal {a} $中电位角度变化的角度变化。该方法可用于找到BSL电场的精确溶液，用于具有定期分布电位的平面区域的圆形或多边形轮廓。分析结果通过数值计算和有限元方法验证。 关键字：表面电极，生物 - 萨瓦特定律，静电问题，确切的可解决模型。
We present an analytic strategy to find the electric field generated by surface electrode SE with angular dependent potential. This system is a planar region $\mathcal{A}$ kept at a fixed but non-uniform electric potential $V(ϕ)$ with an arbitrary angular dependence. We show that the generated electric field is due to the contribution of two fields: one that depends on the circulation on the contour of the planar region ---in a Biot-Savart-Like (BSL) term---, and another one that accounts for the angular variations of the potential in $\mathcal{A}$. This approach can be used to find exact solutions of the BSL electric field for circular or polygonal contours of the planar region with periodic distributions of the electric potential. Analytic results are validated with numerical computations and the Finite Element Method. Keywords: Surface-electrode, Biot-Savart law, electrostatic problems, exactly solvable models.
