notes6 2317 - Prof. David R. Jackson ECE Dept. Spring 2011...

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Unformatted text preview: Prof. David R. Jackson ECE Dept. Spring 2011 Notes 6 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism Notes prepared by the EM Group University of Houston Review of Coordinate Systems Review of Coordinate Systems x y z P ( x,y,z ) An understanding of coordinate systems is important for doing EM calculations. Kinds of Integrals That Often Occur Kinds of Integrals That Often Occur 2 4 C AB C C v V Q d V E dr R E d R Q dV = = = = l l l l (scalar integral, scalar result) (vector integral, scalar result) (vector integral, vector result) (scalar integral, scalar re Line integrals: Volume integrals: 2 4 v V R E dV R = sult) (vector integral, vector result) 2 4 s S S s S Q dS I J n dS R E dS R = = = (scalar integral, scalar result) (vector integral, scalar result) (vector integral, vector result) Surface integrals: We wish to be able to perform all of these in various coordinates. Rectangular Coordinates Rectangular Coordinates r xx yy zz = + + Short hand: ( 29 , , r x y z = Note: Different notations are used for vectors in the books. dx dy dz dS = dxdy dS = dxdz dS = dydz dV dx dy dz = x y z r P ( x,y,z ) Rectangular (cont.) Rectangular (cont.) dr x dx y dy z dz = + + Path Integral (need dr ) Note on notation: The symbol dl is often used instead of dr x y z A B C dr r r +dr r xx yy zz = + + Cylindrical Coordinates Cylindrical Coordinates . x y ( 29 2 2 1 cos sin tan / x y z z x y y x z z - = = = = + = = x y z . z P ( , , z ) Cylindrical (cont.) Cylindrical (cont.) Unit Vectors Note: and depend on ( x, y ) x y $ x y z . $ z This is why we often prefer to express them in terms of x y and Note: A unit vector direction is defined by increasing one coordinate variable while keeping the other two fixed. 1 2 1 1 cos cos x A x x A y x A x A = + = = = Expressions for unit vectors (illustrated for ) 2 cos 2 sin A y = =- = Hence cos sin x y = + x y...
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notes6 2317 - Prof. David R. Jackson ECE Dept. Spring 2011...

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