EE2011 Lecture 1 - Review of Vector Calculus

Electromagnetics electromagnetics curl of a vector

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Unformatted text preview: ua Le-Wei Li, EM Research Group Prof ˆ Bx y 30 z Bz x ˆ z By x Bx y EE2011: Engineering Electromagnetics Electromagnetics Curl of a Vector Field • Vector Identities Involving the Curl – Distributive property of two vector fields AB A B – Divergence of a curl of a vector field A0 – Curl of a gradient of a scalar field V0 Prof Joshua Le-Wei Li, EM Research Group Prof 31 EE2011: Engineering Electromagnetics Electromagnetics Curl of a Vector Field • Curl operator in Cylindrical and Spherical Coordinate Systems – Cylindrical Coordinate System A – Spherical Coordinate System A Prof Joshua Le-Wei Li, EM Research Group Prof 1 R 2 sin 32 ˆ r 1 rr Ar ˆr ˆ z rA z Az ˆ r ˆR ˆ R sin R AR RA R sin A EE2011: Engineering Electromagnetics Electromagnetics Curl of a Vector Field • Example 1 Prof Joshua Le-Wei Li, EM Research Group Prof 33 EE2011: Engineering Electromagnetics Electromagnetics Curl of a Vector Field • Example 2 Prof Joshua Le-Wei Li, EM Research Group Prof 34 EE2011: Engineering Electromagnetics Electromagnetics Curl of a Vector Field • Stokes’s Theorem – The Stokes’s Theorem converts the integral of the curl of a vector over an open surface S into a line integral of the vector along the contour C bounding the su...
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