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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 蠁 such that ,
K = constant.
A cylindrical capacitor consists of two long concentric metal cylinders. If there is a charge of k coulombs per meter on the inside cylinder of radius, and coulombs per meter on the outside cylinder of radius,find -k the electric field E between the cylinders. Hint: Use Gauss鈥檚 law and the method indicated in Figure 10.7. What is E inside the inner cylinder? Outside the outer cylinder? (Again use Gauss鈥檚 law.) Find, either by inspection or by direct integration, the potential role="math" localid="1659237306724" such thatfor each of the three regions above. In each case E is not affected by adding an arbitrary constant to. Adjust the additive constant to makea continuous function for all space
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 .
Question: over the surface in Problem 4, where r = ix + jy + kz. Hint: See Problem 10.9.
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.
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