Chapter 10: Q9 P (page 517)
Short Answer
F and E are polar vectors.
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Chapter 10: Q9 P (page 517)
F and E are polar vectors.
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Carry through the details of getting from and . Hint: You need the dot product of and . This is the cosine of an angle between two axes since each eis a unit vector. Identify the result from matrixAin .
Mass of uniform density=1, bounded by the coordinate planes and the plane x +y +x=1 .
Show that, in polar coordinates, thecontravariant component of dsis which is unitless, the physical component of ds is which has units of length, and thecovariant component of ds iswhich has units role="math" localid="1659265070715" .
Find in spherical coordinates by the method used to obtain(8.5)for cylindrical coordinates. Use your result to find for spherical coordinates, the scale factors, the vector ds , the volume element, the basis vectors and the corresponding unit basis vectors . Write the matrix.
Use equations (9.2), (9.8), and (9.11) to evaluate the following expressions. In spherical coordinates .
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