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Physics - gilbert(amg3448 HW01 tsoi(57210 This print-out...

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gilbert (amg3448) – HW01 – tsoi – (57210) 1 This print-out should have 30 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A circular ring made of an insulating material is cut in half. One half is given a charge - q uniformly distributed along its arc. The other half is given a charge + q also uniformly distributed along its arc. The two halves are then rejoined with insulation at the junctions J , as shown. x y - q + q J J - - - - - - - - - - - - - - - - - - + + + + + + + + ++ + + + + + + + + q e If there is no change in the charge distri- butions, what is the direction of the net elec- trostatic force on an electron located at the center of the circle? 1. Toward the top of the page 2. To the right 3. Toward the bottom of the page correct 4. Into the page 5. To the left Explanation: The rejoined system is symmetrical about the diameter perpendicular to the line con- necting two junctions. The electrostatic force is along the direction connecting the two charges (repulsive for charges of the same sign and attractive for charges of the oppo- site sign), so the force on the electron is paral- lel to the symmetrical axis and points toward the positive charge; i.e. , toward the bottom of the page. 002 10.0 points A strong lightning bolt transfers about 26 C to Earth. How many electrons are transferred? The charge on an electron is - 1 . 60218 × 10 - 19 C. Correct answer: 1 . 62279 × 10 20 . Explanation: Let : q = 26 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 | = 26 C | - 1 . 60218 × 10 - 19 C | = 1 . 62279 × 10 20 . 003 10.0 points A particle with charge 5 μ C is located on the x -axis at the point - 4 cm , and a second particle with charge - 3 μ C is placed on the x -axis at - 8 cm . The Coulomb constant is 8 . 9875 × 10 9 N · m 2 / C 2 . 2 4 6 8 10 - 2 - 4 - 6 - 8 - 10 5 μ C - 3 μ C 3 μ C x (cm) What is the magnitude of the total elec- trostatic force on a third particle with charge 3 μ C placed on the x -axis at 2 cm ? Correct answer: 29 . 3592 N. Explanation: Let : q 1 = 5 μ C = 5 × 10 - 6 C , q 2 = - 3 μ C = - 3 × 10 - 6 C , q 3 = 3 μ C = 3 × 10 - 6 C ,
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gilbert (amg3448) – HW01 – tsoi – (57210) 2 x 1 = - 4 cm = - 0 . 04 m , x 2 = - 8 cm = - 0 . 08 m , and x 3 = 2 cm = 0 . 02 m . Coulomb’s law (in vector form) for the elec- tric force exerted by a charge q 1 on a second charge q 3 , written F 13 is F 13 = k e q 1 q 3 r 2 ˆ r 13 , where ˆ r 13 is a unit vector directed from q 1 to q 3 ; i.e. , r 13 = r 3 - r 1 . x 13 = x 3 - x 1 = (2 cm) - ( - 4 cm) = 0 . 06 m x 23 = x 3 - x 2 = (2 cm) - ( - 8 cm) = 0 . 1 m ˆ x 13 = x 3 - x 1 ( x 3 - x 1 ) 2 = +ˆ ı ˆ x 23 = x 3 - x 2 ( x 3 - x 2 ) 2 = +ˆ ı Since the forces are collinear, the force on the third particle is the algebraic sum of the forces between the first and third and the second and third particles. F = F 13 + F 23 = k e q 1 r 2 13 ˆ r 13 + q 2 r 2 23 ˆ r 23 q 3 = 8 . 9875 × 10 9 N · m 2 / C 2 × (5 × 10 - 6 C) (0 . 06 m) 2 (+ˆ ı ) + ( - 3 × 10 - 6 C) (0 . 1 m) 2 (+ˆ ı ) × (3 × 10 - 6 C) = 37 . 4479 N + ( - 8 . 08875 N) = 29 . 3592 N , with a magnitude of 29 . 3592 N .
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