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Unformatted text preview: nanni (arn437) – HW #7 – Erskine – (56905) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A circular coil enclosing an area of 136 cm 2 is made of 280 turns of copper wire as shown in the figure. A 5 . 4 Ω resistor is inserted in the copper wire. Initially, a uniform magnetic field of magnitude 1 . 49 T points horizontally from left-to-right through the perpendicular plane of the coil. When viewed from the right the coil is wound counter-clockwise. R Magnetic Field B ( t ) During a 7 . 6 minute time interval the field uniformly changes at a constant rate, until a reversed field is reached equal in magnitude to the initial field. How much charge flows through the coil? Correct answer: 2 . 10145 C. Explanation: Let : A = 136 cm 2 , N = 280 turns , R = 5 . 4 Ω , B = 1 . 49 T , and t = 7 . 6 minute , By Faraday’s and Ohm’s laws, E = − N d Φ B dt I R = − N d Φ B dt . We can solve for Q , Since I ≡ dQ dt , dQ = − N R d Φ B integraldisplay dQ = − N R integraldisplay d Φ B Q = − N R A integraldisplay B f B dB = − N R A ( B f − B ) = − parenleftbigg 280 turns 5 . 4 Ω parenrightbigg (0 . 0136 m 2 ) × bracketleftBig ( − 1 . 49 T) − (1 . 49 T) bracketrightBig = 2 . 10145 C . Note: The time it takes to reverse the field is not relevant. 002 (part 1 of 2) 10.0 points Two concentric circular loops of radii b and 2 b , made of the same type of wire, lie in the plane of the page, as shown. The total resistance of the wire loop of radius b is R b = R . b 2 b What is the resistance of the wire loop of radius 2 b ? 1. R 2 b = 2 R correct 2. R 2 b = R 2 3. R 2 b = 4 R nanni (arn437) – HW #7 – Erskine – (56905) 2 4. R 2 b = R 4 5. R 2 b = R Explanation: Since the two loops are made of the same wire, the total resistances are proportional to the length of the wires (the circumference of the loops). ℓ b = 2 π b , and ℓ 2 b = 2 π (2 b ) = 4 π b = 2 ℓ b . Thus, the total resistance of the wire loop of radius 2 b is R 2 b = 2 R . 003 (part 2 of 2) 10.0 points A uniform magnetic field vector B that is perpen- dicular to the plane of the page now passes through the loops, as shown. B B B B b 2 b a The field is confined to a region of radius a , where a < b , and is changing at a constant rate. The induced emf in the wire loop of radius b is E b = E . What is the induced emf in the wire loop of radius R 2 b = 2 b ? 1. E 2 b = 0 2. E 2 b = E 2 3. E 2 b = 4 E 4. E 2 b = 2 E 5. E 2 b = E correct Explanation: E = − d Φ B dt , where Φ B is the magnetic flux through the wire loop. Since b > a , the magnetic flux through both wire loops is exactly the same. Thus, the induced emf in the wire loop of radius 2 b is also E 2 b = E ....
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This note was uploaded on 11/02/2011 for the course PHYSICS 317L taught by Professor Erskine during the Fall '11 term at University of Texas at Austin.
- Fall '11