Physics 4322 Homework Set 2 January 24, 2012 Due: Tuesday, January 31, 2012 1. A wire has resistance R. Determine the resistance of a wire twice the length and half the diameter, assuming it is made from the same material. 2. A conducting sphere of radius ais embedded in a large volume filled with a material with conductivity . The sphere is held a constant potential Vowith respect to the boundary, which may be assumed to be at infinity. Determine the current density J(r), the total current I, and the resistance R. (Hint: Laplace’s equation for Vmust be satisfied.) 3. Two concentric conducting spherical shells having inner and outer radii aand b, respectively, are separated by a weakly conducting material of conductivity . (a) If the potential difference between the spheres is V, what current Iexists between the spheres? (b) What is the resistance Rbetween the shells? 4. Suppose the conductivity of a material between two concentric cylinders is given by (s) = k/s. Calculate the resistance Rbetween the cylinders.
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