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Unformatted text preview: PHY2049 Spring 2009 Profs. D. Acosta, A. Rinzler, S. Hershfield Exam 2 Solutions 1. What is the magnitude and direction of the magnetic field at the origin of the shown arrangement of current-carrying wires. Each wire carries a current of i and points either into or out of the page as indicated, and each wire is a distance d from the origin. Answer: i d ( i + j ) Solution: Each wire produces a magnetic field at the origin of magnitude o i/ (2 d ). The two wires on the x-axis each produce magnetic fields in the j direction. The two wires on the y-axis each produce magnetic fields in the i direction. Sum the four magnetic fields to get the net magnetic field at the origin. 2. A wire is bent into the shown planar shape and carries a current i = 15 mA along the indicated directions. What is the magnitude of the magnetic field at the center of the loop, C if the radius of the loop is R = 5 cm? Answer: 1 . 3 10 7 T Solution: The wire produces a magnetic field coming out of the page at C, and the loop produces a magnetic field going into the page at C. The net field into the page at C is B C = o i 2 R- o i 2 R . 3. A solenoid that is 50 cm long with a radius of 1 cm is to be constructed such that it has a field strength of 0.04 T within its volume. If a current of 3A can be provided, how many windings of a wire in total are required for the entire solenoid to achieve this field? Answer: 5300 Solution: The magnetic field inside a long solenoid is B = o iN/L , where N is the number of turns to be determined and L = 0 . 5 m. 4. Two straight parallel power lines are separated by a distance of 2m. Each carries a current of 5000A, but in opposite directions. What is the magnitude of the force per unit length on the wires, and is the force attractive or repulsive? Answer: 2.5 N/m, repulsive Solution: The force is repulsive because the currents are in opposite directions, and the force per unit length is o i 2 / (2 r ). 5. A solid cylindrical wire of radius 2mm carries a current of 10A distributed uniformly throughout its cross section. What is the magnitude of the magnetic field inside the wire at a radius of 1mm from the central axis?is the magnitude of the magnetic field inside the wire at a radius of 1mm from the central axis?...
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