HourExamIReviewProblems-02-10-08

HourExamIReviewProblems-02-10-08 - Physics 21 Spring 2008...

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Physics 21 Spring 2008 February 10, 2008 Hour Exam I Review Review I-1. ••11. In Fig. 21-24 , three charged particles lie on an x axis. Particles 1 and 2 are fixed in place. Particle 3 is free to move, but the net electrostatic force on it from particles 1 and 2 happens to be zero. If , what is the ratio ? Solution: 21-11. With rightwards positive, the net force on q 3 is ( ) 1 3 2 3 3 13 23 2 2 23 12 23 . q q q q F F F k k L L L = + = + + We note that each term exhibits the proper sign (positive for rightward, negative for leftward) for all possible signs of the charges. For example, the first term (the force exerted on q 3 by q 1 ) is negative if they are unlike charges, indicating that q 3 is being pulled toward q 1 , and it is positive if they are like charges (so q 3 would be repelled from q 1 ). Setting the net force equal to zero L 23 = L 12 and canceling k , q 3 and L 12 leads to 1 1 2 2 0 4.00. 4.00 q q q q + = = − Review I-2 ••31. Figure 22-50 a shows a nonconducting rod with a uniformly distributed charge +Q . The rod forms a half-circle with radius R and produces an electric field of magnitude at its center of curvature P . If the arc is collapsed to a point at distance R from P (Fig. 22-50 b ), by what factor is the magnitude of the electric field at P multiplied? Solution: 22-31. First, we need a formula for the field due to the arc. We use the notation λ for the charge density, λ = Q /L . Sample Problem 22-3 illustrates the simplest approach to circular arc field problems. Following the steps leading to Eq. 22-21, we see that the general result (for arcs that subtend angle θ ) is [ ] arc 0 0 2 sin( / 2) sin( / 2) sin( / 2) 4 4 E r r λ λ θ θ θ πε πε = = .
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