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HW11-Solutions - Version PREVIEW – HW11 – feng...

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Unformatted text preview: Version PREVIEW – HW11 – feng – (58230) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. Displacement Current 03 001 (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 ) 4. RC Q e t/ ( RC ) 5. Q RC e − t/ ( RC ) correct 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 ) = Q e − 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 ) . Note that the displacement current equals the actual current in the wires to the capacitor. Thus, the Ampere-Maxwell law tells us that vector B will be the same regardless of which current we evaluate. 002 (part 2 of 2) 10.0 points Given C = 2 μ F, Q = 28 μ C, R = 391 kΩ, and ǫ = 8 . 85419 × 10 − 12 C 2 / N · m 2 , at what rate is the electric flux between the plates changing at time t = 0 . 17 s? Correct answer:- 3 . 2538 × 10 6 Vm / s. Explanation: Let : ǫ = 8 . 85419 × 10 − 12 C 2 / N · m 2 , t = 0 . 17 s , C = 2 μ F , Q = 28 μ C = 2 . 8 × 10 − 5 C , and R = 391 kΩ = 3 . 91 × 10 5 Ω . From the discussion in the previous part, we know that d Φ E dt = I d ǫ =- Q ǫ RC e − t/ ( RC ) =- 2 . 8 × 10 − 5 C ǫ (3 . 91 × 10 5 Ω) (2 × 10 − 6 F) × e bracketleftbigg- . 17 s (3 . 91 × 10 5 Ω)(2 × 10 − 6 F) bracketrightbigg =- 3 . 2538 × 10 6 Vm / s . Which Maxwell Equation 003 (part 1 of 6) 10.0 points Which of Maxwell’s equations can be used, along with a symmetry argument, to calculate the electric field of a point charge? 1. contintegraldisplay vector B · d vectors = μ I + μ ǫ ∂ Φ E ∂t 2. contintegraldisplay vector E · d vectors =- ∂ Φ B ∂t 3. contintegraldisplay vector B · d vectors = 0 4. contintegraldisplay vector E · d vectors = Q ǫ Version PREVIEW – HW11 – feng – (58230) 2 5. contintegraldisplay vector B · d vector A = μ I 6. contintegraldisplay vector E · d vector A =- ∂ Φ B ∂t 7. contintegraldisplay vector B · d vector A = Q ǫ 8. contintegraldisplay vector E · d vector A = Q ǫ correct 9....
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HW11-Solutions - Version PREVIEW – HW11 – feng...

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