homework 06-solutions

homework 06-solutions - Reilly(mar3978 homework 06...

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Reilly (mar3978) – homework 06 – Turner – (56725) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points A cubic box oF side a , oriented as shown, con- tains an unknown charge. The vertically di- rected electric feld has a uniForm magnitude E at the top surFace and 2 E at the bottom surFace. a E 2 E How much charge Q is inside the box? 1. Q encl = 0 2. Q encl = 2 ǫ 0 E a 2 3. Q encl = 1 2 ǫ 0 E a 2 4. insu±cient inFormation 5. Q encl = ǫ 0 E a 2 correct 6. Q encl = 3 ǫ 0 E a 2 Explanation: Electric ²ux through a surFace S is, by con- vention, positive For electric feld lines going out of the surFace S and negative For lines going in. Here the surFace is a cube and no ²ux goes through the vertical sides. The top receives Φ top = - E a 2 (inward is negative) and the bottom Φ bottom = 2 E a 2 . The total electric ²ux is Φ E = - E a 2 + 2 E a 2 = E a 2 . Using Gauss’s Law, the charge inside the box is Q encl = ǫ 0 Φ E = ǫ 0 E a 2 . 002 10.0 points A closed surFace with dimensions a = b = 0 . 555 m and c = 0 . 8325 m is located as in the fgure. The electric feld throughout the region is nonuniForm and given by v E = ( α + β x 2 ı where x is in meters, α = 3 N / C, and β = 3 N / (C m 2 ). E y x z a c b a What is the magnitude oF the net charge enclosed by the surFace? Correct answer: 1 . 32313 × 10 - 11 C. Explanation: Let : a = b = 0 . 555 m , c = 0 . 8325 m , α = 3 N / C , and β = 3 N / (C m 2 ) .
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homework 06-solutions - Reilly(mar3978 homework 06...

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