Solutions6 - PHYSICS 222 SECTION 1 EXAM 3 SOLUTIONS Part...

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PHYSICS 222 - SECTION 1 EXAM 3 - SOLUTIONS April 13, 2011 Part 1. [14pt] Two wires of length m, labeled 1 and 2 in the figure, are connected to batteries as shown, each with emf The resistance of the wire on the left is and the resistance of the wire on the right is unknown. The separation of the wires is mm. And the force between the wires is N. Assume all wires except the two parallel ones are far apart, and all other resistance in the circuit is negligible. (a) [2pt] What is the direction of the magnetic field due to the current in the long wire on the left at the location of the long wire on the right? At the location of wire 2, the magnetic field due to wire 1 is into the page . The current flows upward through wire 1, so the field lines make circles around it that come out of the page on the left, and into the page on the right of wire 1. (b) [2pt] Is the force between the wires attractive or repulsive? The force on wire 2 due to the magnetic field from wire 1 is with directed upward along the wire and directed into the page, so that the force on wire 2 is to the left. This is an attractive force. 1 2
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2 (c) [3pt] If the current flowing in the circuits on the left and right are and , respectively, what is the magnitude of the magnetic field due to wire 1 at the location of wire 2? Express this in terms of the appropriate symbols , and justify the result using Ampere’s Law . By Ampere’s Law, applied to a circle of radius about wire 1, Therefore, (d) [7pt] Find the unknown resistance numerically. Show your work and all equations used, and include correct units.
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