# hw_week8 - Homework for week 8 Due Thu 3/31(in class...

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Homework for week 8 Due Thu 3/31 (in class) Instructions: Please explain your reasoning in detail. State where the formulas are coming from, and why they are applicable here. (The goal is, after all, so that we can check and possibly correct your way of thinking.) Please write legibly, and draw large and clearly labeled sketches. 14. ( “Mutual inductance of two rings”.) Two circular loops of wire share a common axis of symmetry – which we’ll denote as x axis – as shown in the figure below. A larger loop of radius R 1 is at the coordinate origin. A smaller loop of radius R 2 < R 1 is at the distance x from the coordinate origin, where x R 1 . A current I 1 runs in the larger loop, with the direction indicated on the figure. Due to a large distance between the loops, we can assume that the magnetic field is nearly uniform through the second, smaller loop. (a) What is the magnetic field ~ B 1 ( x ) (both magnitude and orientation) of the first loop at the location of the second loop? (b) What is the flux of that field through the second loop, Φ 2 ? (c) If I 1 changes in time, what is the emf E 2 induced in the second loop? What is the coeficient of mutual inductance, M , between the two loops? (d) If I 1 is constant in time, but the smaller loop is instead moving away from the larger loop with a constant velocity v = dx/dt , what is the emf E 0 2 induced in the second loop? Draw a sketch of the system and indicate the direction of the induced current in the second loop.

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• Fall '11
• Haase
• Ode, Magnetic Field, rod

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