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Chapter 6: Q6P (page 314)
For a simple closed curve Cin the plane show by Green’s theorem that the area inclosed is
The solution to this problem is that the condition is satisfied and the area is inclosed.
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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’s law and the method indicated in Figure 10.7. What is E inside the inner cylinder? Outside the outer cylinder? (Again use Gauss’s 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
Find the torque about the point (1, -2, 1) due to the forceF = 2 i - j + 3 kacting at the point ( 1, 1, -3)
Write out the equations corresponding to (9.3) and (9.4) for Q=2Xbetween points 3 and 4 in Figure 9.2, and add them to get (9.6).
(a) Find the directional derivative of in the direction at the point .
(b)Find the equation of the tangent plane and the equations of the normal line to at the point .
where C is as selected.
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