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# exam2sol - PHY2049 Spring 2011 Profs P Avery S Hersheld...

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PHY2049 Spring 2011 Profs. P. Avery, S. Hershfield Exam 2 Solution 1. Charges Q 1 > 0 and Q 2 < 0 have velocities in the plane of the page as indicated in the figure. A uniform magnetic field with magnitude B is going into the plane of the page, and a uniform electric field with magnitude E is going up (towards the top of the page). If the speed of charge 1 satisfies v 1 > E/B and the speed of charge 2 satisfies v 2 < E/B , what is the direction of the net force on charges 1 and 2? (Up means towards the top of the page, and down means toward the bottom of the page.) Answer: The net force on both particles is down. Solution: For particle 1 the magnetic force is larger because v 1 B > E . Since Q 1 > 0 and vectorv 1 × vector B is down, the net force on particle 1 is down. (The electric force on particle 1 is up.) For particle 2 the electric force is larger because E > v 2 B . Both the electric force and the net force on particle 2 are down. (The magnetic force on particle 2 is also down.) 2. A current carrying square loop of wire is placed in a uniform magnetic field pointing to the right (see figure). If the magnetic moment is is pointing up, what is the direction of the current flow in the wire segment closest to you labeled by i in the figure and which direction will the loop rotate (clockwise or counterclockwise)? Answer: i to the right; rotate clockwise Solution: For a current carrying loop, the direction of the magnetic moment is obtained by wrapping your fingers in the direction of the current and your thumb points in the direction of the magnetic moment. (Always use your right hand.) Thus, the current in the front segment of the wire is to the right. Since the magnetic moment wants to align with the magnetic field ( U = - vectorμ · vector B ), the loop will rotate clockwise. 3. A uniform magnetic field is going into the plane of the page. Two charge particles move in circles in the plane of the page as shown in the figure. The two particles have the same magnitude of charge, | q | , and the same kinetic energy. Which of the following is true about the particles’ charges and masses? Answer: q 1 > 0, m 1 > m 2 Solution: On the right side of the circular path of particle one, the velocity is up and the force is to the left. Since the magnetic field is going into the page, vectorv 1 × vector B is to the left, which is the same direction as the force. Consequently, q 1 is positive. For circular motion we have F = mv 2 /r = qvB or solving for the kinetic energy mv 2 / 2 = qvBr/ 2. Because the particles have the same kinetic energy, particle 1 with the larger radius, has the smaller velocity and the larger mass.

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exam2sol - PHY2049 Spring 2011 Profs P Avery S Hersheld...

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