quiz1solutions - PHYS 2B Quiz 1 Solutions Aris 1 Problem 1...

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PHYS 2B Quiz 1 Solutions Aris January 15, 2010 1 Problem 1 To find x 0 , solve for k (3 q ) x 2 0 + k ( - q ) ( x 0 - a ) 2 = 0 (1) The first term is the field due to the charge at the origin; the second due to the charge at distance a from the origin. Sum the two fields to get the net field, and set it to zero. 2 Problem 2 Immediately to the right of the negative charge, the field is very negative, be- cause the influence of the negative charge is strongest at such small distances. As x increases away from the negative charge, the field due to the negative charge dies as 1 / ( r 2 ) and the field due to the charge 3q begins to dominate. At distance 2 . 4 a , the fields exactly cancel out. The field will rise to a positive value as x increases further. It peaks then approaches zero as we take x to infinity. To find this peak, d dx ( k (3 q ) x 2 + k ( - q ) ( x - a ) 2 ) = 0 (2) We obtain 3( x - a ) 3 = x 3 . Going further, 3 0 . 333 ( x - a ) = x , from which we solve for x = 3 . 3 a . 3 Problem 3 The charge configuration can be split into a point charge 2 q , which has a field that dies as 1 /d 2
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