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Unformatted text preview: PHY2049 Fall 2010 Profs. S. Hershfield, A. Petkova Exam 4 Solution 1. Four charges are arranged as shown in the figure. Each charge is 8 cm from the origin. The values of the charges are Q 1 = +3 C , Q 2 = +1 C , Q 3 = +1 C , and Q 4 = 1 C . What is the magnitude of the force on a fifth charge of 2 C placed at the origin? Answer: 8 N Solution: The xcomponent of the force is F x = k (3 C 1 C )(2 C ) /r 2 , and the ycomponent of the force is F y = k (1 C  1 C )(2 C ) /r 2 , where r = 8 cm . The magnitude of the force at the origin is radicalBig F 2 x + F 2 y . 2. A wire segment of length L has constant linear charge density &gt; 0. Which of the following expressions gives the magnitude of the electric field a distance D from the center of the wire (see figure)? Answer: integraldisplay L/ 2 L/ 2 kD ( x 2 + D 2 ) 3 / 2 dx Solution: This problem is identical to one from Exam 1  see that solution. 3. A point charge lies at the center of two concentric conducting shells, as shown in the figure. What is the surface charge density of the outer surface of the largest shell? Answer: 12 C/m 2 Solution: A Gaussian sphere just larger than the outer shell encloses a net charge of 3 nC, while a sphere inside the outer shell encloses no net charge because the electric field is zero inside a conductor. This means that the net charge on the outer surface of the largest shell is 3 nC. Divide this by the area of a sphere to obtain = ( 3 nC ) / (4 r 2 ). 4. Charges are arranged on a square of side 3 cm as shown in the figure. If Q = 2 . 3 10 7 C , how much work is required to move a charge of 2 Q from infinity to the center of the square? Answer: 0.12 J Solution: The potential, V , at the center of the square is the sum of kQ i /r i , where r i is the distance from charge Q i to the center. For the corners this distance is (3 cm ) / 2, while for the charges on the sides the distance is (3 cm ) / 2. The work to move 2 Q from infinity to the center of the square is ( 2 Q ) V . 5. If the voltage across the entire capacitor network at right is 5.0 V, what is the charge on the 12 F capacitor?...
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 Fall '08
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 Physics, Charge, Light, Electric charge, NC

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