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Unformatted text preview: soto (rrs946) – Homework 1 – Hoffmann – (56605) 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points There are two identical small metal spheres with charges 53 . 3 μ C and − 46 . 8994 μ C. The distance between them is 5 cm. The spheres are placed in contact then set at their original distance. Calculate the magnitude of the force be tween the two spheres at the final posi tion. The value of the Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . Correct answer: 36 . 8201 N. Explanation: Let : q A = 53 . 3 μ C = 5 . 33 × 10 − 5 C , q B = − 46 . 8994 μ C = − 4 . 68994 × 10 − 5 C , and d = 5 cm = 0 . 05 m . When the spheres are in contact, the charges will rearrange themselves until equi librium is reached. Each sphere will then have half of the original total charge: q = q A + q B 2 = 5 . 33 × 10 − 5 C − 4 . 68994 × 10 − 5 C 2 = 3 . 20031 × 10 − 6 C . The force between the two spheres is F = k q 2 d 2 = ( 8 . 98755 × 10 9 N · m 2 / C 2 ) × (3 . 20031 × 10 − 6 C) 2 (0 . 05 m) 2 = 36 . 8201 N . 002 10.0 points Charge Q is on the y axis a distance a from the origin and charge q is on the x axis a distance d from the origin. What is the value of d for which the x component of the force on q is the greatest? 1. d = 0 2. d = √ 2 a 3. d = a 4. d = q Q a 2 5. d = a 2 6. d = q Q √ 2 a 7. d = q Q a √ 2 8. d = a √ 2 correct 9. d = q Q a Explanation: We have the force on charge q on the x axis due to charge Q on the y axis vector F = 1 4 π ǫ q Q r 2 ˆ r , where r = radicalbig a 2 + d 2 . So the x component of the force on q is F x = 1 4 π ǫ q Q r 2 cos θ = 1 4 π ǫ q Q a 2 + d 2 d √ a 2 + d 2 = 1 4 π ǫ q Q d ( a 2 + d 2 ) 3 / 2 . For maximum x component of the force, ∂ F x ∂d = 0 is required. Therefore ∂F x ∂d = q Q 4 π ǫ a 2 − 2 d 2 ( a 2 + d 2 ) 5 / 2 = 0 a 2 − 2 d 2 = 0 d = a √ 2 . soto (rrs946) – Homework 1 – Hoffmann – (56605) 2 003 (part 1 of 2) 10.0 points A strong lightning bolt transfers about 23 . 17 C to Earth. How many electrons are transferred? The charge on an electron is − 1 . 602 × 10 − 19 C. Correct answer: 1 . 44632 × 10 20 . Explanation: Let : q = 23 . 17 C and q e = − 1 . 602 × 10 − 19 C . The charge is proportional to the number of electrons, so q = n  q e  n = q  q e  = 23 . 17 C − 1 . 602 × 10 − 19 C  = 1 . 44632 × 10 20 . 004 (part 2 of 2) 10.0 points The lightning bolt discharge lasts one mil lisecond. What is the average current flowing from the cloud to ground? Correct answer: 23170 A. Explanation: Let : t = 1 ms = 0 . 001 s ....
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This note was uploaded on 11/10/2011 for the course PHYSICS 303L taught by Professor Hoffman during the Fall '11 term at University of Texas.
 Fall '11
 HOFFMAN
 Charge, Work

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