电磁场与电磁波重点概念总结

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1、电磁场与电磁波重点概念总结总结电磁场与电磁波总结第一章一、矢量代数A?B=ABcos?A?B=eABABsin?A?(B?C)=B?(C?A)=C?(A?B)A??B?C??B?A?C??C?A?C?二、三种正交坐标系1.直角坐标系矢量线元dl?exx?eyy?ezz矢量面元dS?exdxdy?eydzdx?ezdxdy体积元dV=dxdydz单位矢量的关系ex?ey?ezey?ez?exez?ex?ey2.圆柱形坐标系矢量线元dl?e?d??e??d??ezdzl矢量面元dS?e??d?dz?ez?d?d?体积元dV??d?d?dz单位矢量的关系e??e??ez3.球坐标系矢量线元

2、dl=erdr+e?rd??e?rsin?d?矢量面元dS=err2sin?d?d?2体积元dV?rsin?drd?d?单位矢量的关系er?e??e?e??ez=e?ez?e??e?e??e?=ere??er?e?三、矢量场的散度和旋度1.通量与散度??2.环流量与旋度?SA?dSdivA???A??v?0?limSA?dS?v??3.计算公式??A???lte=nA?dlroA?S?0A?dl??lilmax?S?Ax?xex?Ay?yey??yAy?A??Az1?1?A?1?1?1?A2(?A?)??(rAr)?(sin?A?)???A?2z??A????????zr?rrsin

3、???rsin????zez??A??A?e?1?A?e????ez??zAz??A?er12e????e????rsin?Az??A??xAx?Ar???rsin??r?A?rA?4.矢量场的高斯定理与斯托克斯定理??四、标量场的梯度1.方向导数与梯度SA?dS??V??AdV??A?dl??lS??Ad?S?u?lP0?limu(M)?u(M0)?l?l?0?u?lP0??u?xcos???u?yco?s?u?zc?os-1-?u?el??ucos?graud?2.计算公式?u?ex?u?nen?ex?u?x?ey?u?y+z?u?z?u?x?ey?u?y?ez?u1?u?u?e

4、?u?e????????z?ez?u?z?u?er?u?r?e?1?ur???e?1?ursin??z五、无散场与无旋场1.无散场??(??A)六、拉普拉斯运算算子1.直角坐标系?0F???A2.无旋场??(?F?-?uu)?0?u??Ax?x2222?u?x?22?2?u?y22??u?z222?A?ex?Ax?ey?Ay?ez?Az?Ay?x22222?Ax?2.圆柱坐标系2??Ax?y2?Ax?z2，?Ay?2??Ay?y22??Ay?z222，?Az?2?Az?x22??Az?y22??Az?z221???u?1?u?u?u??????222???????????z22?2?

5、212?A??12?A??22?A?e???A??2A??2??e???A??2A??2??ez?Az????????????3.球坐标系1??2?u?1???u?1?u?u?2?sin???2?r??222r?r??r?rsin???????rsin???22?A???222cot?2?A?22??A?er??Ar?2Ar?A???222?rrr??rsin???????22?Ar12cos??A????e???A??2?2A??222??????rrsin?rsin????2?Ar212cos??A????e???A??A?????22222????rsin?rsin?rsin?

6、??七、亥姆霍兹定理如果矢量场F在无限区域中处处是单值的，且其导数连续有界，则当矢量场的散度、旋度和边界条件（即矢量场在有限区域V’边界上的分布）给定后，该矢量场F唯一确定为F(r)????(r)???A(r)其中?(r)?14??V???F(r?)1dV?A(r)?r?r?4??V???F(r?)?r?r?第二章一、麦克斯韦方程组1.静电场真空中：??E?dS=Sq?0=1?0?V?dV（高斯定理）??lE?dl?0??E???00??E?场与位：E(r)?14??0?r?r'r?r'V'?(r')dV'E?????(r)?3-2-14π?0

7、??(r?)V?

8、r?r?

9、dV介质中：??D?dS?qS??lE?dl?0??D????E?0极化：D??0E?PD?(1??e)?PS?Pn?Pe?0E???0E??E?n?P????Pr2.恒定电场电荷守恒定律：sJ?ds??dqdt??ddt?V?dv??J???t?0传导电流与运流电流：J??EJ??v恒定电场方程：??J?dS?0S??lJ?dl?0??J?0??J=03.恒定磁场真空中：??B?dl??0I（安培环路定理）l??SB?dS?0