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Unformatted text preview: Problem Set 01 Note: The following problem set is designed to test your knowledge in calculus and basic physics like classical mechanics, electromagnetism and gravity. The problem set is due September 12 by midnight. Please return directly to me in my office Rutherford 321. If I’m not there slip your assignment below my door. 1. In d + 1 dimension the electromagnetic potential between two charges is given by the following formula: V ( r ) = V- e 2 4 π² · 1 r ² (1) where V is a constant potential (whose detail is irrelevant for this problem) and e is some numerical constant which, in the limit when ² → 1, becomes the charge in d = 3 dimensions. Determine the value of d , the dimension, in the limit when ² → 0 so that V ( r ) would describe the correct potential in that dimension. What happens in the other extreme limit ² → - 1? 2. Find dy dx of the following functions assuming the fact that both x and y are never singular: (a) y = x (sin x ) x (sin x ) .... (b) y y y = x x + x x x + a a x + y x y , a > where a is a constant and the dots represent an infinite sequence of the given pattern....
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