Homework 1-solutions

# Homework 1-solutions - soto(rrs946 – Homework 1 –...

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Unformatted text preview: soto (rrs946) – Homework 1 – Hoffmann – (56605) 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 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.

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Homework 1-solutions - soto(rrs946 – Homework 1 –...

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