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Find the potential inside and outside a spherical shell of radius R (Figure shown), which carries a uniform surface charge. Set the reference point at infinity.

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Consider a thin, uniformly charged rod of length L with total charge Q and test points A, a distance a from the center of the rod and B a distance b from the rod. Find the potential difference between A and B first by integrating the point source potential to find VA and VB and subtracting, and then by integrating the field. Compare the results in the limit of L>>(a and b). To test the far field limit, compare the appropriate result to the case where L is much less than both a and b. You may need to do this one numerically.
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Some practice with an infinite line charge. (a) What is the electric field on an infinite line charge that has a constant charger per unit length of X? (b) What is the electrostatic potential in this case? Is it possible to make the potential vanish at infinity? (c) Consider an infinite conducting cylinder of radius a that is grounded. Suppose there is an infinite line charge with a constant charge per unity length that is located inside the cylinder, such that it is parallel to the cylinder, but displaced from the central axis by an amount b, with b < a. Determine the electrostatic potential everywhere inside the cylinder. I suggest using the method of images, by placing another line charge outside the cylinder.