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Unformatted text preview: ragsdale (zdr82) – HW8 – ditmire – (58335) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A conductor consists of an infinite number of adjacent wires, each infinitely long and carrying a current I (whose direction is out-of- the-page), thus forming a conducting plane. A C If there are n wires per unit length, what is the magnitude of vector B ? 1. B = μ I 2 2. B = 4 μ I 3. B = 2 μ nI 4. B = 4 μ nI 5. B = μ I 6. B = 2 μ I 7. B = μ nI 4 8. B = μ I 4 9. B = μ nI 2 correct 10. B = μ nI Explanation: l W A C B B By symmetry the magnetic fields are equal and opposite through point A and C and hori- zontally oriented. Following the dashed curve in a counter-clockwise direction, we calculate contintegraldisplay vector B · dvectors , which by Ampere’s law is propor- tional to the current through the dashed loop coming out of the plane of the paper. In this problem this is a positive current. Hence vector B along the horizontal legs points in the di- rection in which we follow the dashed curve. Ampere’s Law is contintegraldisplay vector B · dvectors = μ I . To evaluate this line integral, we use the rect- angular path shown in the figure. The rectan- gle has dimensions l and w . The net current through the loop is nI l . Note that since there is no component of vector B in the direction of w , we are only interested in the contributions along sides l contintegraldisplay vector B · dvectors = 2 B l = μ nl I B = μ nI 2 . 002 10.0 points A superconducting solenoid has 5810 turns / m and carries a current of 2000 A. What is the magnetic field generated inside the solenoid? The permeability of free space is 1 . 25664 × 10 − 6 T · m / A. Correct answer: 14 . 6021 T. Explanation: Let : n = 5810 turns / m , μ = 1 . 25664 × 10 − 6 T · m / A , and I = 2000 A . ragsdale (zdr82) – HW8 – ditmire – (58335) 2 The magnetic field generated inside the solenoid is B = μ nI = ( 1 . 25664 × 10 − 6 T · m / A ) × (5810 turns / m) (2000 A) = 14 . 6021 T . keywords: 003 (part 1 of 2) 10.0 points A capacitor of capacitance C has a charge Q at t = 0. At that time, a resistor of resistance R is connected to the plates of the charged capacitor. Find the magnitude of the dis- placement current between the plates of the capacitor as a function of time. 1. Q RC e − t/Q 2. RC Q e t/ ( RC ) 3. Q RC e − t/ ( RC ) correct 4. Q RC e t/ ( RC ) 5. RC Q e − t/ ( RC ) Explanation: Basic Concept RC circuits. Displacement Current. The displacement current is defined to be I d = ǫ d Φ E dt . The electric field inside a capacitor is essen- tially uniform and E = q ǫ A . Since the charge on a capacitor in a discharging RC circuit is given by q ( t ) = Qe − t/RC , the displacement current is found by I d = ǫ d Φ E dt = ǫ d dt parenleftbigg q ǫ A A parenrightbigg = dq dt = − Q RC e − t/ ( RC ) ....
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- Spring '10
- Magnetic Field, loop, ragsdale