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Chapter 6: Q2P (page 313)
around the square with vertices
The integral will give the solution to be 40.
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Verify that the force field is conservative. Then find a scalar potential such that
Verify that the force field is conservative. Then find a scalar potential 蠁 such that ,
K = constant.
Given the vector.
(a) Find .
(b) Evaluate over a rectangle in the plane bounded by the lines .
(c) Evaluate around the boundary of the rectangle and thus verify Stokes' theorem for this case.
Use either Stokes' theorem or the divergence theorem to evaluate each of the following integrals in the easiest possible way.
Expand the triple product for given in the discussion of Figure 3.8. If is perpendicular to (Problem 16), show that , and so find the elementary result that the acceleration is toward the center of the circle and of magnitude .
Given and
(a) Are these forces conservative? Find the potential corresponding to any conservative force.
(b) For any nonconservative force, find the work done if it acts on an object moving from (-1,-1)to (1,1)along each of the paths shown.
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