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4. Griffiths 3.8. (3.7 in 3rd Ed.) In part (b), in addition to direct integration, use Gauss's law to show that the tota
Posted: Sun Jul 17, 2022 5:36 pm
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- 4 Griffiths 3 8 3 7 In 3rd Ed In Part B In Addition To Direct Integration Use Gauss S Law To Show That The Tota 1 (77.56 KiB) Viewed 39 times
4. Griffiths 3.8. (3.7 in 3rd Ed.) In part (b), in addition to direct integration, use Gauss's law to show that the total induced surface charge has to be equal to the image charge. Problem 3.8 (a) Using the law of cosines, show that Eq. 3.17 can be written as follows: V(r, ) = 41€0r2 + a2 - 2ra cos 0 R2 + (ra/R)2 - 2ra cose (3.19) where r and 8 are the usual spherical polar coordinates, with the z axis along the line through q. In this form, it is obvious that V = 0 on the sphere, r = R. (b) Find the induced surface charge on the sphere, as a function of e. Integrate this to get the total induced charge. (What should it be?)