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solution1_pdf - harvey(zmh93 Homework 1 Homann(56745 This...

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harvey (zmh93) – 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 27 . 5 μ C and 19 . 119 μ 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: 24 . 6602 N. Explanation: Let : q A = 27 . 5 μ C = 2 . 75 × 10 5 C , q B = 19 . 119 μ C = 1 . 9119 × 10 5 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 = 2 . 75 × 10 5 C 1 . 9119 × 10 5 C 2 = 4 . 19051 × 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 ) × (4 . 19051 × 10 6 C) 2 (0 . 08 m) 2 = 24 . 6602 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 = a 2 correct 3. d = a 2 4. d = q Q a 2 5. d = q Q 2 a 6. d = 2 a 7. d = q Q a 2 8. d = a 9. d = 0 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 0 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 0 q Q r 2 cos θ = 1 4 π ǫ 0 q Q a 2 + d 2 d a 2 + d 2 = 1 4 π ǫ 0 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 0 a 2 2 d 2 ( a 2 + d 2 ) 5 / 2 = 0 a 2 2 d 2 = 0 d = a 2 .
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harvey (zmh93) – Homework 1 – Hoffmann – (56745) 2 003 (part 1 of 2) 10.0 points A strong lightning bolt transfers about 23 . 93 C to Earth. How many electrons are transferred? The charge on an electron is 1 . 60218 × 10 19 C. Correct answer: 1 . 49359 × 10 20 . Explanation: Let : q = 23 . 93 C and q e = 1 . 60218 × 10 19 C . The charge is proportional to the number of electrons, so q = n | q e | n = q | q e | = 23 . 93 C |− 1 . 60218 × 10 19 C | = 1 . 49359 × 10 20 .
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