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First Midterm with Solutions

First Midterm with Solutions - 1 F irst M idterm P HYI32...

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1 First Midterm PHYI32, Oct. 8,2010 PRINT yom name and indicate yom recitation section (M, W or TH):~/.<I? / ~ / / 6.' /"/1 ~ '£"""--7_/"/",v"/ '/r-;i 1 .' Prob.l Prob.2 Prob. 3 Total Express your solution through formulas; explain the logic of what you do, and substitute numbers, if required, only at the end. We will take points off if you do not show your solution in terms of formulas before showing your calculations, Points will be also taken off for excessive or insufficient precision and for the absent or wrong units at the ends of calculations. Problem 1: Calculating potential and field from a continuous charge distribution [35 points] Electric charge Q is uniformly distributed over a straight line extending from zero to d on the x- axis: ~~ c\ -+}Z:: .. :::.--------- (-- ~', oAdtr- 0 \p ~~illR1&Wf;¥ttjHW~Iitt~MMtWl1:~;, .) X 1 ' ' qtL : p I I I V d .... - - - - - - - - - - - - - - - - - ..... - - - - - - - - - - - - - - - - .-' I I ~ a). Prove that electric potential V p at a point P on an x axis is given by Vp (p) = KQ In(1 +!! .... ) d P where p is the distance from the end of the charged line to point P [You will need to set up and evaluate an integral over infinitesimal contributions dV p from intervals of lengths dx of the charged line. Show all your work
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