quiz3 - balanced if Q/q 1 =[p(1 p 2 The problem above is a...

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Quiz III PHY2054/3808 9/10/09 1. Two positive free point charges q and 4q are a distance L = 7.12 m apart. A third charge Q is placed so that the entire system is in equilibrium. Find the ratio Q/q. First, note that the charge sign of Q has to be different than that on the other two charges. Otherwise (with all charges of the same sign) the problem has no solution. We find the location of Q so that the forces acting on it from the other two charges cancel. Calling x the distance from the q charge, we get from balance of forces the relation kQq/x 2 = k4Qq/(L - x) 2 , which gives L -x = 2x or x = L/3. To find Q, we have to adjust it until the forces acting on the other charges are both zero. Balance of forces on the q charge gives the force condition kqQ/x 2 = k4q 2 /L 2 . Using x = L/3 and solving yields Q/q = 4/9. Note that the same value of Q also balances the force on the 4q charge. Suppose that the two charges are q 1 and q 2 with the ratio q 2 /q 1 = p 2 . Can you show that the forces are
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Unformatted text preview: balanced if Q/q 1 =- [p/(1+p)] 2. . The problem above is a special case of p =2. 2. A conducting spherical shell has inner radius r and outer radius R . A point charge of −q is located at the center of the sphere and a charge of + Q is placed on the conducting shell. What is the surface charge density at the outer surface of the conducting shell? The charge in the shell will distribute itself on the inner and outer surfaces in such a way that the field inside the conductor is zero. Using Gauss’ law, we draw an imaginary surface inside the shell (radius between r and R). Since the total flux through the surface is zero, the total enclosed charge is zero and therefore the charge on the inner surface must be q (to cancel the charge −q in the center). Thus the total charge on the outer surface is Q−q. The outer charge density is therefore (Q−q)/4πR 2 . This quiz was replaced by two problems from the book (Serway and Vuille), 16.8 and 16.24....
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