81. (II) Find the electric field along the axis of a uniformly charged ring of radius R and total charge Q by taking the appropriate derivatives of the potential found in Example 24–9. Set up the problem by using the direct integration techniques presented in Chapter 23. Compare the difficulties of the two ways of calculating the electric field. 85. (II) Two concentric metal shells of radii r 1 and r 2 respectively carry charge q 1 and q 2 respectively. Assuming r 1<r2, what is the potential in the range 0 <=r<=inf ? 88. (II) A large, square plane with sides of length L , parallel to the yz-plane and ocated at x 1, has charge density sigma 1. A similar plane, located at x 2 , has charge density sigma2. How much work must be done to bring the second plane to within a distance a of the first one? Neglect end effects; that is, calculate the fields as though the planes were infinite. 7 . Calculate the capacitance of two concentric spherical conductors of radii r and R , respectively. 19.
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