MidTermkey - PHYS 1304 Mid-term Exam Name ID 1(Total 30...

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1 PHYS 1304 Mid-term Exam Name ID 1. (Total 30 points) Two point charges, q 1 and q 2 , are fixed in space. The distance between the two charges is d . Here q 1 = 2.0 μC, q 2 = 8.0 μC, and d = 9.0 cm. 1 μC = 10 -6 C. (a, 20 points) Find the point in space that is close to the two charges where the electric field is 0. (b, 10 points) Now you move a charge q 3 from infinitely far away to this point, how much work you have to do during this process when q 3 = 1.0 μC? The Coulomb constant k e = 8.99×10 9 N · m 2 /C 2 . (c, bonus 5 points, do it when you have time in the end) Is q 3 in a stable or unstable equilibrium condition? Would your answer change if q 3 = -1.0 μC? q 1 q 2 p o x 9.0 cm x 2 e q E k r = One dimensional problem. Construct the coordinate as shown. For (a) the formula to use is The equation: ( 29 1 2 2 2 9 0 e e q q k k x . x = - ( 29 2 2 2 0 8 0 9 0 . . x . x = - or: Solve for x , we have 3 0 cm or 9 0 cm (discard) x . x . = = - So x = 3.0 cm is the point where the electric field is 0. For (b), the formula to use is e qQ U k r = Electric potential energy q 3 of when it is infinitely far away is 0. The work
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