介电系数对平行板电容器电容的影响

Influence of dielectric coefficient on the capacitance of parallel-plate capacitor

电容器电容的计算是电磁理论的重要内容,是大学物理课程中的教学重点和难点.采用高斯定理法和修正拉普拉斯方程法对平行板电容器电容进行求解,给出C=ε_r((ε_0S)/d)的条件并计算了填充2种不同ε_r电介质后的电容.结果表明,在均匀、线性、各向同性电介质中,介电系数ε为常数,平行板电容器的电容满足C=ε_r((ε_0S)/d);在非均匀、线性、各向同性电介质中,介电系数ε_r(x)为标量函数,平行板电容器的电容C≠ε_r((ε_0S)/d).在平行板电容器中填充2种不同ε_r电介质后,总电容相当于2个电容器串联.

Calculation of the capacitance of capacitors is an important part of the electromagnetic theory,and it is both the key and difficult point in the course of college physics.The capacitance of parallel-plate capacitor are studied in the Gauss theorem method and the modified Laplace′s equation method,the C=εrε0S/d under a certain conditionεr was calculated.The results show that in homogeneous and linear isotropic dielectric,the dielectric coefficient were given,and the capacitance of two differentεis constant,the capacitance of parallel-plate capacitor given satisfy the C=εrε0S/d.Under inhomogeneous and linear isotropic dielectric condition,the dielectric coefficienteεr(x)is scalar function,the capacitance of parallel-plate capacitor given satisfy the C≠εrε0S/d.When the parallel-plate capacitor is filled with two different dielectricsεr,the total capacitance is equivalent to two capacitors in series.