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In an experiment we placed a long dielectric cylindrical shell (cylindrical tube)(with inner and outer radii r1 and r2, respectively) in a homogenous field such that its axis was orthogonal to the field. The medium elsewhere has a dielectric constant of unity.

How can I calculate the potentials and fields everywhere?

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""cylindrical shell"" what is that? –  Georg Nov 30 '11 at 9:14
    
Its basically a solid cylinder with radius r2 minus the solid cylinder with radius r1 (r1<r2) –  Rebel Nov 30 '11 at 15:27
    
Mhmmmm, do You fear writing "tube" for some reason? Did You wow not to use it? For the problem, look for pictures of field lines in textbooks. My gut feeling is, that this problem is engineering-like (really complicated and disgusting). Up to the seventies such problems were solved in electrolytic tanks, since the 70ties the method of fined elements on computers is used. –  Georg Nov 30 '11 at 15:38
    
Its apparently solved using elementary electrodynamics, or so im told –  Rebel Nov 30 '11 at 17:54
    
Contra Georg I guess this is probably solvable analytically. Have you tried just solving Laplace's equation in cylindrical coordinates and matching the boundary conditions? –  BebopButUnsteady Nov 30 '11 at 17:55

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