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Problem 3: Imagine you have a very thin plastic hoop of diameter D, which is charged up to total net electrostatic charge Q. The hoop is thin in the sense that the plastic rod of which it is made has a diameter d < D. Computing the electric field everywhere from this hoop is hard! But there are three places that are easy. Compute the electric field (possibly in a limit, or approximately) at these three locations, and give a clear argument for your answer in each case: (a) exactly at the center of the hoop; (b) at a position that is a very small perpendicular distance ri from some point on edge of the hoop, such that d D. In each case, give the magnitude and direction of the field. You might need to use words (rather than formulae) to express the direction unambiguously.

Problem 3: Imagine you have a very thin plastic hoop of diameter D, which is charged up to total net electrostatic charge Q. The hoop is thin in the sense that the plastic rod of which it is made has a diameter d < D. Computing the electric field everywhere from this hoop is hard! But there are three places that are easy. Compute the electric field (possibly in a limit, or approximately) at these three locations, and give a clear argument for your answer in each case: (a) exactly at the center of the hoop; (b) at a position that is a very small perpendicular distance ri from some point on edge of the hoop, such that d D. In each case, give the magnitude and direction of the field. You might need to use words (rather than formulae) to express the direction unambiguously.

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Problem 3: Imagine you have a very thin plastic hoop of diameter D, which is charged up to total net electrostatic charge Q. The hoop is thin in the sense that the plastic rod of which it is made has a diameter d < D. Computing the electric field everywhere from this hoop is hard! But there are three places that are easy. Compute the electric field (possibly in a limit, or approximately) at these three locations, and give a clear argument for your answer in each case: (a) exactly at the center of the hoop; (b) at a position that is a very small perpendicular distance r from some point on edge of the hoop, such that d < r< D; and (c) at very large distance R, such that R> D. In each case, give the magnitude and direction of the field. You might need to use words (rather than formulae) to express the direction unambiguously. Assume that there are no other charges anywhere!
Transcribed Image Text:Problem 3: Imagine you have a very thin plastic hoop of diameter D, which is charged up to total net electrostatic charge Q. The hoop is thin in the sense that the plastic rod of which it is made has a diameter d < D. Computing the electric field everywhere from this hoop is hard! But there are three places that are easy. Compute the electric field (possibly in a limit, or approximately) at these three locations, and give a clear argument for your answer in each case: (a) exactly at the center of the hoop; (b) at a position that is a very small perpendicular distance r from some point on edge of the hoop, such that d < r< D; and (c) at very large distance R, such that R> D. In each case, give the magnitude and direction of the field. You might need to use words (rather than formulae) to express the direction unambiguously. Assume that there are no other charges anywhere!
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