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Chapter 6: Q17P (page 295)
Find, , where , using (6.7) and also using (6.3). Show that your results are the same by using (4.11) and (4.12).
The solution to this problem is .
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over the upper half of the sphere , if .
Draw a figure similar to figurebut with q outside the surface. A vector (like rin the figure) fromq to the surface now intersects it twice, and for each solid angle there are two where renters and where it leaves the surface. Show that is given by (10.21) for the whereleaves r the surface and the negative of(10.21)for thewhere renters the surface. Hence show that the totalover the closed surface is zero.
over the surface consisting of the four slanting faces of a pyramid whose base is the square in the (x,y) plane with corners at , and whose top vertex is at (1,1,2) where.
Evaluate each of the integrals in Problems to as either a volume integral or a surface integral, whichever is easier.
over the region , where localid="1657282505088"
Verify that the force field is conservative. Then find a scalar potential such that .
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