Homework_11-solutions

# Homework_11-solutions - toupal(rgt374 Homework 11...

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toupal (rgt374) – Homework 11 – Chiu – (58295) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 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. RC Q e t/ ( RC ) 2. Q RC e t/Q 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 0 d Φ E dt . The electric field inside a capacitor is essen- tially uniform and E = q ǫ 0 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 0 d Φ E dt = ǫ 0 d dt parenleftbigg q ǫ 0 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 = 4 μ F, Q = 29 μ C, R = 252 kΩ, and ǫ 0 = 8 . 85419 × 10 12 C 2 / N · m 2 , at what rate is the electric flux between the plates changing at time t = 0 . 2 s? Correct answer: 2 . 66452 × 10 6 Vm / s. Explanation: Let : ǫ 0 = 8 . 85419 × 10 12 C 2 / N · m 2 , t = 0 . 2 s , C = 4 μ F , Q = 29 μ C = 2 . 9 × 10 5 C , and R = 252 kΩ = 2 . 52 × 10 5 Ω . From the discussion in the previous part, we know that d Φ E dt = I d ǫ 0 = Q ǫ 0 RC e t/ ( RC ) = 2 . 9 × 10 5 C ǫ 0 (2 . 52 × 10 5 Ω) (4 × 10 6 F) × e bracketleftbigg 0 . 2 s (2 . 52 × 10 5 Ω)(4 × 10 6 F) bracketrightbigg = 2 . 66452 × 10 6 Vm / s . 003 10.0 points What is the fundamental source of electro- magnetic radiation? 1. None of these 2. current 3. any charge 4. voltage 5. an accelerating charge correct Explanation: The fundamental source of electromagnetic radiation is oscillating electric charges, which emit oscillating electric and magnetic fields.

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toupal (rgt374) – Homework 11 – Chiu – (58295) 2 004 10.0 points According to Maxwell’s equation, the speed of light in a vacuum is 1. greater for radio waves than for visible light. 2. a function of the distance from the source. 3. independent of frequency. correct 4. greater for visible light than for radio waves. 5. a function of the size of the source. Explanation: Application of Faraday’s Law and the Ampere-Maxwell equation to EM radiation results in the prediction that the speed of light is c = 1 μ 0 ǫ 0 , independent of frequency. 005 10.0 points Gamma-ray bursters are objects in the uni- verse that emit pulses of gamma rays with high energies. The frequency of the most en- ergetic bursts has been measured at around 3 . 0 × 10 21 Hz.
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