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14. Two very long (practically infinite) conducting cylindrical rods of radius R run parallel to one another. Their central axes are a distance D apart.

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14. Two very long (practically infinite) conducting cylindrical rods of radius R run parallel to one another. Their central axes are a distance D apart. You may assume D > 2R. They carry linear charge density (charge per meter) A and -A respectively. Recall that the electric field strength due to a long cylinder is given by E(r) = 2TEor (for r > R). Your goal in this question is the calculate the capacitance per meter of this setup. The following steps will help you, although you are not required to follow them exactly. (1) Sketch this setup. Then write down the definition of capacitance. Your goal then is to express the potential difference in terms of A. (2) Find the total electric field along the straight line between the two centers. You may want to express this in terms of some variable r, which measures the distance from one of the centers. (3) Having the electric field, you can find the potential difference using AV = / E. de, with appropriately chosen limits

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