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q4s - Physics 2212 K Summer 2009 Quiz#4 Solutions...

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Physics 2212 K Quiz #4 Solutions Summer 2009 ² 0 Permittivity constant m p Mass of a proton μ 0 Permeability constant m e Mass of an electron e Fundamental charge c Speed of light K Coulomb constant g Acceleration due to gravity Unless otherwise directed, friction, drag, and gravity should be neglected, and all batteries and wires are ideal. Any integrals in free-response problems must be evaluated. I . (24 points) An infinite slab of current has thickness t and uni- form area current density J out of the page. What is the magnitude of the magnetic field at a distance d above the sheet? Express your answer in terms of parameters defined in the problem, and physical or mathematical constants. . . . . . . . . . . . . . Symmetry considerations show that the magnetic field points to the left above the slab, and to the right below it. Use Ampere’s Law. Sketch a rectangular Amperian Loop of height 2 d + t and width s . Then I ~ B · ~ ds = B 2 s as ~ B is parallel to ~ ds at the top and bottom of the loop, and ~ B is perpendicular to ~ ds on the left and right sides. The current passing through the loop can be found from the current density I through = Z ~ J · ~ dA = JA = Jst Putting these together in Ampere’s Law I ~ B · ~ ds = μ 0 I through B 2 s = μ 0 Jst B = μ 0 Jt/ 2 Quiz #4 Solutions Page 1 of 4
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1. (8 points) The switch in the illustrated circuit is set to position “b” for a long time, then set to position “a” for a time t a , then set back to position “b”. After that, the current through the resistor is I = I 0 e - t b /RC where t b is the time from returning the switch to position “b”.
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