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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 xaxis. 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 q3is ()13233132322231223.q qq qFFFkkLLL=+=++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 q3by q1) is negative if they are unlike charges, indicating that q3is being pulled toward q1, and it is positive if they are like charges (so q3would be repelled from q1). Setting the net force equal to zero L23=L12 and canceling k, q3and L12leads to 11220 4.00.4.00qqqq+=⇒= −Review I-2 ••31. Figure 22-50ashows a nonconducting rod with a uniformly distributed charge +Q. The rod forms a half-circle with radius Rand produces an electric field of magnitude at its center of curvature P. If the arc is collapsed to a point at distance Rfrom P(Fig. 22-50b), by what factor is the magnitude of the electric field at Pmultiplied? Solution: 22-31. First, we need a formula for the field due to the arc. We use the notation λfor 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 []arc002sin(/ 2)sin(/ 2)sin(/ 2)44Errλλθθθπεπε=−−=.
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