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Chapter 3: Q3.23P (page 150)
A spherical shell of radius carries a uniform surface charge on the "northern" hemisphere and a uniform surface charge on the "southern "hemisphere. Find the potential inside and outside the sphere, calculating the coefficients explicitly up to and .
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For the infinite slot (Ex. 3.3), determine the charge density on the strip at , assuming it is a conductor at constant potential .
Find the potential outside a charged metal sphere (charge Q, radius R) placed in an otherwise uniform electric field E0 . Explain clearly where you are setting the zero of potential.
Two point charges, 3q and -q, are separated by a distance a. For each of the arrangements in Fig. 3.35, find (i) the monopole moment, (ii) the dipole moment, and (iii) the approximate potential (in spherical coordinates) at large r (include both the monopole and dipole contributions).
Two infinite parallel grounded conducting planes are held a distancepart. A point chargeis placed in the region between them, a distance fromone plate. Find the force on Check that your answer is correct for the special
cases and .
a) Using the law of cosines, show that Eq. 3.17 can be written as follows:
Where and are the usual spherical polar coordinates, with the z axis along the
line through . In this form, it is obvious that on the sphere, .
b) Find the induced surface charge on the sphere, as a function of . Integrate this to get the total induced charge. (What should it be?)
c) Calculate the energy of this configuration.
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