Problem 3.43 A conducting sphere of radius a, at potential V., is surrounded by a thin concentric spherical shell of rad

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Problem 3 43 A Conducting Sphere Of Radius A At Potential V Is Surrounded By A Thin Concentric Spherical Shell Of Rad 1 (35.82 KiB) Viewed 28 times

Problem 3.43 A conducting sphere of radius a, at potential V., is surrounded by a thin concentric spherical shell of radius b, over which someone has glued a surface charge o(@) = k cose, where k is a constant and is the usual spherical coordinate. (a) Find the potential in each region: (i) r > b, and (ii) a <r <b. (b) Find the induced surface charge 0;() on the conductor. (c) What is the total charge of this system? Check that your answer is consistent with the behavior of V at large r. aVo/r+(b – a )k cos/3r'€, r>b Answer: V(r, ) = aVo/r + (r? – a )k cos e/3r²€, r<b