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oldmidterm 01-solutions

# oldmidterm 01-solutions - marout(ssm979 – oldmidterm 01...

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Unformatted text preview: marout (ssm979) – oldmidterm 01 – Turner – (56725) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Three equal charges of 8 μ C are in the x- y plane. One is placed at the origin, another is placed at (0.0, 12 cm), and the last is placed at (33 cm, 0.0). Calculate the magnitude of the force on the charge at the origin. The Coulomb constant is 9 × 10 9 N m 2 / C 2 . Correct answer: 40 . 3482 N. Explanation: Let : q = 8 μ C = 8 × 10 − 6 C , ( x 1 , y 1 ) = (0 , 12 cm) = (0 , . 12 m) , ( x 2 , y 2 ) = (33 cm , 0) = (0 . 33 m , 0) and ( x , y ) = (0 , 0) . The electric fields are E y = k e q x 2 1 + y 2 1 = ( 9 × 10 9 N m 2 / C 2 )( 8 × 10 − 6 C ) 0 + (0 . 12 m) 2 = 5 × 10 6 N / C , and E x = k e q x 2 2 + y 2 2 = ( 9 × 10 9 N m 2 / C 2 )( 8 × 10 − 6 C ) (0 . 33 m) 2 + 0 = 6 . 61157 × 10 5 N / C , Thus E = radicalBig E 2 x + E 2 y and F = q E = q radicalBig E 2 x + E 2 y = ( 8 × 10 − 6 C ) · radicalBig (5 × 10 6 N / C) 2 + (6 . 61157 × 10 5 N / C) 2 = 40 . 3482 N . 002 10.0 points A point charge q 1 is concentric with two spher- ical conducting thick shells, as shown in the figure below. The smaller spherical conduct- ing shell has a net charge of q 2 and the larger spherical conducting shell has a net charge of q 3 . q 3 q 2 q 1 R 1 R 2 R 3 R 4 R 5 r 1 r 2 r 3 r 4 Hint: Under static conditions, the charge on a conductor resides on the surface of the conductor. What is the charge Q r 3 on the inner surface of the larger spherical conducting shell? 1. Q r 3 = + q 1 + q 2 2. Q r 3 = 0 3. Q r 3 = − q 1 − q 2 − q 3 4. Q r 3 = − q 1 5. Q r 3 = + q 1 + q 2 + q 3 6. Q r 3 = − q 1 − q 2 correct 7. Q r 3 = − q 1 + q 2 8. Q r 3 = + q 1 9. Q r 3 = − q 1 − q 2 + q 3 10. Q r 3 = + q 1 − q 2 marout (ssm979) – oldmidterm 01 – Turner – (56725) 2 Explanation: The net charge inside a Gaussian surface located at r = R 4 must be zero, since the field in the conductor must be zero. Therefore, the charge on the inner surface of the large spherical conducting shell must be − ( q 1 + q 2 ). 003 10.0 points A circular arc has a uniform linear charge density of 6 nC / m. The value of the Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . 2 5 9 ◦ 2 . 6 m x y What is the magnitude of the electric field at the center of the circle along which the arc lies? Correct answer: 32 . 0078 N / C. Explanation: Let : λ = 6 nC / m = 6 × 10 − 9 C / m , Δ θ = 259 ◦ , and r = 2 . 6 m . θ is defined as the angle in the counter- clockwise direction from the positive x axis as shown in the figure below. 1 2 9 . 5 ◦ 1 2 9 . 5 ◦ r vector E θ First, position the arc symmetrically around the y axis, centered at the origin. By symmetry (in this rotated configuration) the field in the x direction cancels due to charge from opposites sides of the y-axis, so E x = 0 ....
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oldmidterm 01-solutions - marout(ssm979 – oldmidterm 01...

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