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homework10 - ECE 3025 Homework 10 Inductance Faradays Law 1...

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ECE 3025 Homework 10: Inductance & Faraday’s Law 1. A perfectly conducting filament containing a small 500Ω resistor is formed into a square, as illustrated below. Find I ( t ) if B = (a) 0 . 3 cos(120 πt 30 z Teslas; (b) 0 . 4 cos[ π ( ct y )]ˆ z µ T, where c = 3 × 10 8 m/s. x y 500 W I t ( ) B 0.5 m 2. The rails in the figure below each have a resistance of 2.2 Ω/m. The bar moves to the right at a constant speed of 9 m/s in a uniform magnetic field of 0.8 T. Find I ( t ), 0 < t < 1s, if the bar is at x = 2m at t = 0 and: (a) a 0.3Ω resistor is present across the left end with the right end open-circuited; (b) a 0.3Ω resistor is present across each end. B B 16 m v 0.2 m I t ( ) 3. Using first-principles in field theory, calculate the per-unit-length inductance and capacitance of a transmission line consisting of two parallel wires whose axes are separated by b units of length and have a radius of a units of length. Assume the current is carried on the surface of the conductive wires. Also calculate the intrinsic impedance and velocity of propagation. 4. Inductive RFID: Inductive radio frequency identification (RFID) is finding more and more applications in anti-shoplifting devices, keyless entry systems, prescription drug authentication,

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and fare card tracking – to name just a few. One such application of RFID that is near-and-dear to many Georgia Tech students is the new MARTA BreezeWay system. The system replaces the old token system with an RFID fare card that keeps track of rides on the MARTA with a small computer chip that contains an electronically erasable and programable read-only memory (EEPROM). When a rider approaches the new BreezeWay turnstyle, the card is brought in proximity to a side panel containing a loop of wires. This scenario is illustrated below: z y x L Current, NI L MARTA RFID Fare Card Square Reading Coil The current in the reader coil oscillates at 13.56 MHz and, following Faraday’s Law, excites a voltage around the coil in the fare card. This voltage is then rectified by the chip to provide power to the memory and communication circuitry. Based on this scenario and the following specifications, answer the following questions.
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