homework 06-solutions - howard (cah3459) homework 06 Turner...

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howard (cah3459) – homework 06 – Turner – (56705) 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 = 1 2 & 0 Ea 2 2. Q encl =2 & 0 2 3. Q encl =3 & 0 2 4. Q encl =0 5. insu±cient inFormation 6. Q encl = & 0 2 correct 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 = - 2 (inward is negative) and the bottom Φ bottom 2 . The total electric ²ux is Φ E = - 2 +2 2 = 2 . Using Gauss’s Law, the charge inside the box is Q encl = & 0 Φ E = & 0 2 . 002 10.0 points A closed surFace with dimensions a = b = 0 . 435 m and c . 5655 m is located as in the fgure. The electric feld throughout the region is nonuniForm and given by ' E =( α + β x 2 ı where x is in meters, α = 5 N / C, and β = 2 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: 2 . 72015 × 10 - 12 C. Explanation: Let : a = b . 435 m , c . 5655 m , α = 5 N / C , and β = 2 N / (C m 2 ) . The electric feld throughout the region is directed along the x -axis and the direction oF d ' A is perpendicular to its surFace. ThereFore, ' E is parallel to d ' A
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homework 06-solutions - howard (cah3459) homework 06 Turner...

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