Physics 1 Problem Solutions 189

Physics 1 Problem Solutions 189 - Chapt 23 The Electric...

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Chapt. 23 The Electric Field 185 023 qfull 00700 3 3 0 tough math: far-field limit of a charge system 7. Let us consider the electric field in the far-field limit for a localizable system of point charges. In this context localizable means that all the charges can be enclosed in finite closed surface: e.g., a sphere or a box. a) Draw a diagram indicating the charges and in particular a general charge q i . Put an origin someplace within the system of charges. Draw vector vector r i from the origin to q i and also draw a general vector vector r to a point well outside of the system in the far field. The angle between vector r i and vector r is θ i . b) Give the formula for the electric field at vector r due to the whole system. Give it in a form that makes explicit use of the law of cosines. c) Expand in a Taylor’s series about r i /r = 0, the electric field formula to 2nd order in r i /r . Truncate the series to 1st order and then zeroth order in r i /r . HINT: Actually, it’s slightly simpler to Taylor expand about y =
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