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Electromagnetic Field Theory - A Problem-Solving Approach ...

Cartesian Cylindrical Spherical x = r cosc/ S r sin 6 cos 4 = r sin4 S r sin 6 sin4 z = z = rcos6 y ix= Cos Oi-sin4k 4 = sin Ocos ki,+cos 6 cos 4ie -sin Ois iY =sin 0 i,+ Cos 01i = sin 0 sin 6i, + Cos 6 sin ie = S il41+C541 +cos 6 io i1 = cos Oi,-sin Ois Cylindrical Cartesian Spherical =~V Ix+ y7 Sr sin 6 tan~1y/x = z = rcos6 = cos (k ,, +sin i, = sin Oi,+cos 6ie i4 . = -sin ki,,+Cos 4i, = i4 = i, = cos i, -sin iO Spherical Cartesian Cylindrical If,-+z"r I4x +y +z _1 z -1 z0 = Cos = cos = cot-' x/y i, = sinG cos kix+sin 6 sin ci, = sin i, +Cos Oi, +cos i. i, = cos 6 cos oi,+cos 6 sin oi, = Cos Oi,-sin Oi, -sin Oi. i = -sin 46i, +Cos 0i, = i4, Geometric relations between coordinates and unit vectors for Cartesian, cylir drical, and spherical coordinate systems. CartesianCoordinates(x, y, z) Vf = Ofi.+Ofi,+ Ofi. ax ay Oz+-A=,++-iV-aA,, aA, aA, 2 ax ay az aA aA)VxA ay_ a (aA,(-_)+i=i.)

integral and differential field laws. Often the same problem is solved by different methods so that the advantages and limita­ tions of each approach becomes clear. Sample problems and their solutions are presented for each new concept with great emphasis placed on …

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