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Mathematics 317T2 Assignment6

Mathematics 317T2 Assignment6 - Nonetheless find some paths...

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Mathematics 317T2 Assignment #6 due Wednesday, March 3, 2010 1. Suppose the force field F ( x , y , z ) is conservative in the domain D . If ) , , ( z y x ϕ is a potential for F , show that the lines of force for F are perpendicular to the equipotential surfaces const. = 2. Determine whether each of the following vector fields is conservative in 3 R , and find their potentials when conservative. (a) . 2 2 2 k j i F z y x + + = (b) . k j i F xy x y + + = 3. Show that k j i F y x y + + = is not a conservative vector field.
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Unformatted text preview: Nonetheless, find some paths C for which . = ⋅ ∫ C d r F 4. In an electrostatic field due to a point charge q located at the origin, a charge Q is moved from the point (2,3,6) to the point (1,2,2). Find the work done for all possible paths not passing through the origin. Is the question, as worded, ambiguous? Give a reason. Recall Coulomb’s Law....
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