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Unformatted text preview: Alvarado, Patrick – Homework 4 – Due: Feb 16 2007, 11:00 pm – Inst: Opyrchal, H 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points You have a potential difference of 6 V. How much work is done to transfer 0 . 34 C of charge through it? Correct answer: 2 . 04 J. Explanation: Let : V = 6 V and q = 0 . 34 C . The potential difference is V = W q W = V q = (6 V)(0 . 34 C) = 2 . 04 J . keywords: 002 (part 1 of 1) 10 points A uniform electric field of magnitude 286 V / m is directed in the positive x-direction. Sup- pose a 25 μ C charge moves from the origin to point A at the coordinates, (24 cm, 51 cm). x y 286 V / m O A (24 cm , 51 cm) What is the absolute value of the change in potential from the origin to point A ? Correct answer: 68 . 64 V. Explanation: Let : x = 24 cm , y = 51 cm , and k ~ E k = 286 V / m . The potential difference from O to A is defined as Δ V = V A- V O =- Z A O ~ E · d~s. We know that ~ E = (286 V / m) ˆ ı. We need to choose a path to integrate along. Because the electric force is conservative, it doesn’t matter which path we take; they all give the same answer. There are two choices of path for which the math is simple (see the figure below.) x y E O A ( x,y ) I I B I I Path I: V A- V O = ( V A- V B ) + ( V B- V O ) , From O to B, ~ E and d~s are both along the x-axis, so ~ E · d~s = E dx . From B to A, ~ E and d~s are perpendicular, so ~ E · d~s = 0. V A- V O =- Z B O ~ E · d~s- Z A B ~ E · d~s =- Z x E dx- Z y dy =- E Z x O dx =- E Δ x =- (286 V / m)(0 . 24 m) =- 68 . 64 V . The absolute value is | Δ V | = 68 . 64 V . Path II: In this case, ~ E · d~s = E cos θ ds. where cos θ = x l ⇒ x = l cos θ . V A- V O =- E cos θ Z l O ds =- E l cos θ =- E x. which is the same as the result for the other path. Alvarado, Patrick – Homework 4 – Due: Feb 16 2007, 11:00 pm – Inst: Opyrchal, H 2 keywords: 003 (part 1 of 1) 10 points The gap between electrodes in a spark plug is 0 . 087 cm. To produce an electric spark in a gasoline-air mixture, an electric field of 1 . 9 × 10 6 V / m must be achieved. On starting a car, what is the magnitude of the minimum voltage difference that must be supplied by the ignition circuit?...
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This note was uploaded on 06/02/2010 for the course MGMT 121 taught by Professor Morozova during the Spring '10 term at NJIT.
- Spring '10