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Unformatted text preview: Physics 1112 Spring 2010 University of Georgia Instructor: HBSch¨uttler Solution to PHYS 1112 In-Class Exam #2B Thu. March 18, 2010, 11:00am-12:15pm Conceptual Problems Problem 1: A beam of coherent (laser) light of wavelength λ is incident upon a diffraction grating with line spacing d , with λ < d , as shown in the figure below. Assume | Δ y | is the distance (in cm) between the two 1st-order intensity maxima, observed on a screen at a distance L on the other side of the grating. This distance | Δ y | will L Diff. Grating Laser Beam Fig. 2.03 Screen 1st order maxima Δ y θ (A) decrease if we increase L (keeping λ and d fixed); (B) decrease if we increase λ (keeping L and d fixed); (C) decrease if we increase d (keeping λ and L fixed); (D) increase if we decrease λ (keeping L and d fixed); (E) increase if we increase d (keeping λ and L fixed). Answer: (C) At 1st-order maximum: sin θ = λ/d . Also, Δ y = 2 L tan θ , by trigonometry (see Fig. 2.03). So sin θ , hence θ , hence tan θ , hence | Δ y | , will decrease if d increases or if λ decreases. Therefore, (C) is correct; and (B), (D) and (E) are wrong. Because of Δ y = 2 L tan θ , | Δ y | increases if L increases: hence (A) is wrong. Problem 2: If two point charges Q 1 and Q 2 at some distance r repel each other with a force of 160N, what force would they exert on each other if r is quadrupled ( × 4); Q 1 is tripled ( × 3) with unchanged sign; and the sign of Q 2 is reversed ? The two charges will 1 Physics 1112 Spring 2010 University of Georgia Instructor: HBSch¨uttler (A) attract each other with a force of 120N (B) attract each other with a force of 2560N (C) attract each other with a force of 30N (D) repel each other with a force of 2560N (E) repel each other with a force of 30N Answer: (C) By Coulomb’s 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 = 4 r will change F → F = (3 / 4 2 ) × F = (3 / 16) × 160N = 30N. 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. Problem 3: In the figure below, Q 1 and Q 2 are both negative point charges with | Q 1 | and | Q 2 | being of comparable magnitude. Which arrow drawn at P could correctly represent the electric field vector ~ E generated by Q at P ?...
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