Homework 1-solutions - gonzales (pag757) Homework 1...

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Unformatted text preview: gonzales (pag757) Homework 1 Hoffmann (56745) 1 This print-out should have 20 questions. Multiple-choice 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 12 . 8 C and 8 . 96398 C. The distance between them is 8 cm. The spheres are placed in contact then set at their original distance. Calculate the magnitude of the force between the two spheres at the final position. The Coulomb constant is 8 . 98755 10 9 N m 2 / C 2 . Correct answer: 5 . 16611 N. Explanation: Let : q A = 12 . 8 C = 1 . 28 10 5 C , q B = 8 . 96398 C = 8 . 96398 10 6 C , and d = 8 cm = 0 . 08 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 = 1 . 28 10 5 C 8 . 96398 10 6 C 2 = 1 . 91801 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 ) (1 . 91801 10 6 C) 2 (0 . 08 m) 2 = 5 . 16611 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 = q Q a 2. d = 0 3. d = q Q 2 a 4. d = q Q a 2 5. d = a 2 6. d = a 7. d = 2 a 8. d = q Q a 2 9. d = a 2 correct Explanation: We have the force on charge q on the x axis due to charge Q on the y axis vector F = 1 4 q Q r 2 r , where r = radicalbig a 2 + d 2 . So the x component of the force on q is F x = 1 4 q Q r 2 cos = 1 4 q Q a 2 + d 2 d a 2 + d 2 = 1 4 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 a 2 2 d 2 ( a 2 + d 2 ) 5 / 2 = 0 a 2 2 d 2 = 0 d = a 2 . gonzales (pag757) Homework 1 Hoffmann (56745) 2 003 (part 1 of 2) 10.0 points A strong lightning bolt transfers about 26 . 95 C to Earth. How many electrons are transferred? The charge on an electron is 1 . 60218 10 19 C....
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This note was uploaded on 01/27/2012 for the course PHY 303L taught by Professor Turner during the Spring '08 term at University of Texas at Austin.

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Homework 1-solutions - gonzales (pag757) Homework 1...

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