tutorial_calculus - (x, y, z) and cylindrical coordinate (...

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EE1259: Electromagnetic tutorial 1 1 EE1259 Tutorial on Calculus 1. Simplify the following expressions: )] ( [ B A B A r r r r × × × 2. E r and F r are vector fields given by z y x a yz a a x E r r r r + + = 2 and z y x a xyz a y a xy F r r r r + = 2 , determine (a) E r at (1,2,3) (b) The component of E r along F r at (1,2,3) (c) A vector perpendicular to both E r and F r at (0,1,-3) whose magnitude is unity 3. For a scalar function f and a vector function G , prove: ( ) ( ) ( ) G f G f G f r r r + = 4. Variables substitution: Given Cartesian coordinate
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Unformatted text preview: (x, y, z) and cylindrical coordinate ( , , z) , prove that + = = cos sin sin cos y x 5. Verify Stokess theorem for the vector field a a B r r r r sin cos + = By evaluating the following (a). S l d B r r over the contour shown below (both contour a) and b) ) (b). ( ) V s d B r r...
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