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Unformatted text preview: PHY2049 Fall 2010 Profs. S. Hershfield, A. Petkova Exam 1 Solution 1. Four charges are placed at the corners of a rectangle as shown in the figure. If Q 1 = 1 C, Q 2 =- 2 C, Q 3 = 1 C , and Q 4 = 2 C , what is the magnitude of the net force on Q 4 ? Answer: 11.4 N Solution: Make a table showing the components of each of the forces and then add the components. F on 4 by 1- k (1 C )(2 C ) / (3 cm ) 2 F on 4 by 2 +0 . 8 k (2 C )(2 C ) / (5 cm ) 2 +0 . 6 k (2 C )(2 C ) / (5 cm ) 2 F on 4 by 3- k (1 C )(2 C ) / (4 cm ) 2 F total-0.27 N-11.36 N The directions were obtained using opposite charges attract and like charges repel. The factors of 0.8 and 0.6 are the trigonometric factors to determine the x- and y-components. The magnitude of the force is radicalBig F 2 x + F 2 y . 2. Five charges of magnitude e and sign indicated in the figure are placed on a line. The separation between the charges is d . What is the magnitude and direction of the force on the middle charge? Answer: 1.5 ke 2 /d 2 , left Solution: For this problem again use opposite charges attract and like charges repel. Label the charges 1 to 5 from left to right. As for the previous problem it is helpful to make a table: F on 3 by 1 ke 2 / (2 d ) 2 to the right F on 3 by 2 ke 2 / ( d ) 2 to the left F on 3 by 4 ke 2 / ( d ) 2 to the left F on 3 by 5 ke 2 / (2 d ) 2 to the right F total 1.5 ke 2 /d 2 to the left 3. The following tests are made on an object X of unknown charge and material. (i) A positively charged object is attracted to X. (ii) A negatively charge object is attracted to X. Which of the following are possible explanations of this behavior? Answer: X is a neutral conductor. Solution: As demonstrated in class and also in the book (see Fig. 21-4), when a charged object is brought next to a neutral conductor, there is an induced charge near the charged object. For example, a positive charge brought near a neutral conductor will induce a negative charge near the surface of the conductor. The metal will be attracted to the positive charge. The metal will also be attracted to a negative charge because induced charge in this case will be positive. 4. How many excess electrons are in- 2 C charge? Answer: 10 13 Solution: The charge of an electron is- 1 . 6 10- 19 C . (- 2 10- 6 C ) / (- 1 . 6 10- 19 C ) 10 13 . 5. A and B are identical conducting spheres. Sphere A is initially charged to 1 C, and sphere B has no charge initially. The following five steps are done. (i) Sphere A is touched to sphere B ....
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