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HW07-solutions-1

# HW07-solutions-1 - gilbert(amg3448 HW07 tsoi(57210 This...

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gilbert (amg3448) – HW07 – tsoi – (57210) 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A single circular loop of wire in the plane of the page is perpendicular to a uniform magnetic field B directed out of the page, as shown. B B If the magnitude of the magnetic field is increasing, then the induced current in the wire loop is 1. directed upward out of the paper. 2. counterclockwise around the loop. 3. zero. (No current is induced.) 4. directed downward into the paper. 5. clockwise around the loop. correct Explanation: Using Lenz’s law, the induced current must be directed to counter the change of the mag- netic flux through the loop; i.e. , the mag- netic field generated by the induced current is pointing upward out of the page. Thus, using right hand rule, the induced current must be clockwise along the loop. 002 (part 1 of 2) 10.0 points A horizontal circular wire loop of radius 0 . 7 m lies in a plane perpendicular to a uniform magnetic field pointing from above into the plane of the loop, has a magnitude of 0 . 24 T. If in 0 . 14 s the wire is reshaped from a circle into a square, but remains in the same plane, what is the magnitude of the average induced emf in the wire during this time? Correct answer: 0 . 566321 V. Explanation: Let : r = 0 . 7 m , b = 0 . 24 T , and Δ t = 0 . 14 s . The average induced emf E is given by E = N ΔΦ Δ t = ΔΦ Δ t since N = 1, and ΔΦ = B ( A circle - A square ) = B ( π r 2 - A square ) . Also, the circumference of the circle is 2 π r , so each side of the square has a length L = 2 π r 4 = π r 2 , so A square = L 2 = π r 2 2 . Thus ΔΦ = B π r 2 - π r 2 2 = 0 . 24 T π (0 . 7 m) 2 - π (0 . 7 m) 2 2 = - 0 . 079285 T · m 2 . and the average induced emf is E = - - 0 . 079285 T · m 2 0 . 14 s = 0 . 566321 V . 003 (part 2 of 2) 10.0 points The current in the loop during the deforma- tion 1. flows in a direction that cannot be deter- mined from given information.

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gilbert (amg3448) – HW07 – tsoi – (57210) 2 2. flows counter-clockwise when viewed from above. 3. flows clockwise when viewed from above. correct 4. does not arise. Explanation: The deformation causes the flux through the loop to decrease since the area of the loop is reduced. By Lenz’s law, the induced emf will cause the current to flow in the loop so as to induce a magnetic field that attempts to resist the change of magnetic flux through the loop. A clockwise flow of current, when viewed from above tends to increase the ex- isting downward magnetic field through the loop, thereby resisting the decrease of mag- netic flux through the loop. 004 10.0 points Two coils are suspended around a central axis as shown in the figure below. One coil is connected to a resistor with ends labeled a and b . The other coil is connected to a battery E . The coils are moving relative to each other as indicated by the velocity vectors v .
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