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HW5soln - electric potential energy U of the system(Take...

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Physics 21 Fall 2007 Solution to HW-5 Potential Difference and Potential near a Charged Sheet Let A =( x _1, y _1) and B =( x _2, y _2) be two points on the same side of a charged sheet with surface charge density σ . The electric field E has magnitude σ / ε _0) everywhere, and the field points away from the sheet. (A) What is the potential difference V _( AB )= V_A - V_B between points A and B ? (B) If the potential at ±infinity is taken to be zero, what is the value of the potential at A , at some positive distance y _1 from the surface of the sheet? (C) Now take the potential to be zero at y =0 instead of at infinity. What is the value of V_A at point A some positive distance y _1 from the sheet? (A) (B) + infinity: positive work is done against the field. (C) Formula from part (A) gives E (0 - y _1) = - E y _1. Electric Potential Energy of Three Point Charges Three equal point charges, each with charge Q , are placed at the vertices of an equilateral triangle whose sides are of length a
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Unformatted text preview: electric potential energy U of the system? (Take the zero of PE as all three charges infinitely apart). 23.5 A small metal sphere with net (negative) charge q_1 is fixed. A second small metal sphere with a net (negative) charge q_2 is projected toward q_1. When the two spheres are d apart, q_2 is moving toward q_1 with speed v. Treat the two spheres as point charges; ignore gravity. (A) What is the speed of q_2 when the spheres are d' apart? (B) How close do the spheres get? Stopping the Proton An infinitely long line of charge has a linear charge density λ . A proton at distance r _0 from the line is moving directly toward the line with speed v . How close does the proton get to the line of charge? 23.79 Electric charge is distributed uniformly along a thin rod of length a , with total charge Q . Take the potential to be zero at infinity. Find the potential at points R and P . [Here we first do an arbitrary point ( x,y )]....
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