Exam 1 Example

Extra expanding the result 3 in powers of ar 1 and

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Unformatted text preview: , Ex,upper = (R-a/2)3 and Ex,lower = -ke qa , while their total is just (4). (R+a/2)3 Compared to the field of a point charge, which falls off with distance R as R-2 , and of a dipole, which falls off as R-3 , the field of our system falls off faster, as R-4 . This is because both total charge and total dipole moment are zero in this case, our system is what is called (an elementary) quadrupole. 1 2. The field of the infinite line at distance x from it is E(x) = 2ke /x. The force acting on a small element dx of the rod is E(x)(Q/2a)dx, the total force therefore is just r+a r+a ke Q ln . (5) F = E(x)(Q/2a)dx = a r-a r-a When r a, this expression turns into F = 2ke Q/r, as one should expect (the rod looks like a point charge). 3. The electric field E(r) =...
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