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# 303L-HW6 - erro(jmf2547 HW 06 berk(60290 This print-out...

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fierro (jmf2547) – HW 06 – berk – (60290) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A closed surface with dimensions a = b = 0 . 554 m and c = 0 . 6648 m is located as in the figure. The electric field throughout the region is nonuniform and given by vector E = ( α + β x 2 ı where x is in meters, α = 2 N / C, and β = 4 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 . 28109 × 10 11 C. Explanation: Let : a = b = 0 . 554 m , c = 0 . 6648 m , α = 2 N / C , and β = 4 N / (C m 2 ) . The electric field throughout the region is directed along the x -axis and the direction of d vector A is perpendicular to its surface. Therefore, vector E is parallel to d vector A over the four faces of the surface which are perpendicular to the yz plane, and vector E is perpendicular to d vector A over the two faces which are parallel to the yz plane. That is, only the left and right sides of the right rectangular parallel piped which encloses the charge will contribute to the flux. The net electric flux through the cube is ΔΦ = integraldisplay right side E x d A - integraldisplay left side E x d A = a b bracketleftbig α + β ( a + c ) 2 - α - β a 2 bracketrightbig = a b β (2 a c + c 2 ) = a b c β (2 a + c ) = (0 . 554 m) (0 . 554 m) (0 . 6648 m) × [4 N / (C m 2 )] [2 (0 . 554 m) + 0 . 6648 m] = 1 . 44687 N m 2 / C , so the enclosed charge is q = ǫ 0 ΔΦ = [8 . 85419 × 10 12 C 2 / (N m 2 )] × (1 . 44687 N m 2 / C) = 1 . 28109 × 10 11 C . 002 10.0 points Which of the following is true about the net force on an uncharged conducting sphere in a uniform electric field? 1. It produces a torque on the sphere about the direction of the field. 2. It is zero. correct 3. It is in the direction opposite to the field. 4. It causes the sphere to oscillate about an equilibrium position. 5. It is in the direction of the field.

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