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Unformatted text preview: Physics 1112 Spring 2010 University of Georgia Instructor: HBSchuttler Solution to PHYS 1112 In-Class Exam #2A Thu. March 18, 2010, 9:30am-10:45am Conceptual Problems Problem 1: A beam of coherent (laser) light of wavelength is incident upon two parallel slits with spacing d , and with < d , as shown in the figure below. Assume | y | is the distance (in cm) between the two dark fringes (interference intensity minima), observed closest to the central maximum on a screen at a distance L on the other side of the double- slits. This distance | y | will L Double Slit Laser Beam Fig. 2.04 Screen 1st dark fringes y (A) decrease if we decrease L (keeping and d fixed); (B) decrease if we increase (keeping L and d fixed); (C) decrease if we decrease d (keeping and L fixed); (D) increase if we decrease (keeping L and d fixed); (E) increase if we increase d (keeping and L fixed). Answer: (A) At 1st minimum (closest to central maximum): sin = (1 / 2) /d . Also, y = 2 L tan , by trigonometry (see Fig. 2.04). So sin , hence , hence tan , hence | y | , will decrease if d increases or if decreases. Therefore, (B), (C), (D) and (E) are wrong. Because of y = 2 L tan (and is fixed if and d are fixed), | y | decreases if L decreases: hence (A) is correct. Problem 2: If two point charges Q 1 and Q 2 at some distance r repel each other with a force of 10 N, what force would they exert on each other if Q 1 is tripled ( 3) without change of sign; r is doubled ( 2), and the sign of Q 2 is reversed ? The two charges will (A) attract each other with a force of 13 . 33 N 1 Physics 1112 Spring 2010 University of Georgia Instructor: HBSchuttler (B) attract each other with a force of 15 N (C) repel each other with a force of 15 N (D) repel each other with a force of 7 . 5 N (E) attract each other with a force of 7 . 5 N Answer: (E) By Coulombs law, the force F = k | Q 1 || Q 2 | /r 2 | Q 1 | /r 2 . Hence, changing | Q 1 | | Q 1 | = 3 | Q 1 | and r r = 2 r will change F F = (3 / 2 2 ) F = (3 / 4) 10 N = 7 . 5 N. Since Q 1 and Q 2 initially repel each other, they initially have the same sign. Since the sign of Q 1 is unchanged and the sign of Q 2 is reversed, the two charges will have the opposite sign, after Q 1 and Q 2 are changed, and therefore will attract each other....
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