EE2011 Lecture 1 - Review of Vector Calculus

Prof joshua le wei li em research group prof 35 ee2011

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Unformatted text preview: rface S. B ds S B dl C – If B = 0, then the field is said to be conservative or conservative irrotational. Prof Joshua Le-Wei Li, EM Research Group Prof 35 EE2011: Engineering Electromagnetics Electromagnetics Laplacian Operator • Laplacian Operator in Cartesian Coordinates 2 2 V V 2 2 E x 2 2 y V x2 2 2 2 z 2 2 V y2 E V z2 ˆ x 2 Ex ˆ y 2 Ey ˆ z 2 Ez • Laplacian Operator in Cylindrical Coordinates 2 V 1 V r rr r 1 r2 2 V 2 2 V z2 • Laplacian Operator in Spherical Coordinates 2 V 1 2V R 2 R RR 1 R 2 sin Prof Joshua Le-Wei Li, EM Research Group Prof sin 36 V 1 R 2 sin 2 2 V 2 EE2011: Engineering Electromagnetics Electromagnetics Summary • What do the magnitude and direction of the gradient of a scalar quantity represent? • What is the physical meaning of the divergence of a vector field? • What is the meaning of the transformation provided by the divergence theorem? • What is the meaning of the transformation provided by Stoke’s theorem? • When is a vector field “conservative”? Prof Joshua Le-Wei Li, EM Research Group Prof 37 EE2011: Engineering Electromagnetics Electromagnetics...
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