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PHY 021 - PHYS 21 Spring 2011 HW 1 solutions 1 Of the...

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PHYS 21 Spring 2011 HW 1 solutions: 1. Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated a particles. For what value of q / Q >0.5 will the electrostatic force between the two parts have 1/3 of the maximum possible value? Solutions for textbook version problem The magnitude of the force of either of the charges on the other is given by F q Q q r 1 4 0 2 b g where r is the distance between the charges. We want the value of q that maximizes the function f ( q ) = q ( Q q ). Setting the derivative / dF dq equal to zero leads to Q 2 q = 0, or q = Q /2. Thus, q / Q = 0.500. 10. In Fig. 21-24 four particles form a square with edge length a = 2.81 × 10 -2 m. The charges are q 1 = q 4 = 1.18 × 10 -15 C and q 2 = q 3 = q . What is q (in Coulombs) if the net electrostatic force on particle 1 is zero? Solution: For ease of presentation (of the computations below) we assume Q > 0 and q < 0 (although the final result does not depend on this particular choice).
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