Physics 2080 Extra Credit Due March 15, 2011

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1 Physics 2080 Extra Credit Due March 15, 2011 This assignment covers chapters and is worth 10 points extra credit on the final exam. Print these pages and do all work here. Complete the questions and problems and show all work, circling your answer where appropriate. Please be neat and organized with your answers and solutions if I can t read it or follow the solution, I can t grade it. 1. Show below are the positions of two small objects with identical masses and different charges. The smaller charge is fixed in place while the +4q charge with mass m is free to move. At time t 1, the charges are at rest and separated by a distance d. At a later time t 2, the charges are separated by a distance 2d. a. Is the work done by the +q charge on the +4q charge during the time interval positive, negative, or zero? If the work done cannot be determined with the given information, state that explicitly. Explain your reasoning. b. Will the electric potential energy of the system of two charges increase, decrease, or remain the same during the time interval? If the change in electric potential energy cannot be determined with the given information, state that explicitly. Explain your reasoning. c. Will the kinetic energy of the system of the two charges increase, decrease, or remain the same during the time interval? If the change in kinetic energy cannot be determined with the given information, state that explicitly. Explain your reasoning.

2 2. Shown below is a student s drawing of the electric forces acting on object A (with charge +q and mass m) and object B (with charge +4q and mass 4m). There is something wrong with this diagram. Please explain how to correct it. 3. Three positive charges with magnitudes 9 mc, 6 mc, and 3 mc are fixed in place. A student makes the following calculation for the magnitude of the electric field and acting on the 9 mc charge: 6mC E = ( N m 2 C 2 ) (2cm) 3mC 2 (2cm) 2 Draw the arrangement of these three charges and clearly label the point that satisfies this calculation. Explain how your drawing is consistent with the calculation.

3 4. Three long straight wires are parallel to each other and have the same current I into or out of the page as indicated. For the situation shown above, describe how each of the following changes will affect the total magnetic field acting on wire Y. a. The current in wire Y is reversed. b. The directions of the currents in Y and Z are both reversed. c. The currents in wires X and Z are doubled. d. The current in wire Y is reduced to one third of the original. e. The direction of the current in X is reversed. 5. An electron is moving to the right at a velocity v when it enters a region containing a magnetic field. The external magnetic field is uniform and into the paper. The path of the electron in the magnetic field is indicated by the dotted curve. There is at least one error in the diagram. Identify all errors and explain how to correct them.

4 6. A student is asked to design a circuit to supply an electric motor with 1.0 ma of current at 3.0 V potential difference. a. Determine the power to be supplied to the motor. b. Determine the electrical energy to be supplied to motor in 60 s. c. Operating as designed above, the motor can lift a kg mass a distance of 1.0 m in 60 s at a constant velocity. Determine the efficiency of the motor. To operate the motor, the student has available only a 9.0 V battery to use as the power source and the following five resistors: d. In the space below, complete a schematic diagram of a circuit that shows how one or more of these resistors can be connected to the battery and motor so that 1.0 ma and 3.0 V of potential difference are supplied to the motor. Be sure to label each resistor in the circuit with the correct value of its resistance.

5 7. In a linear accelerator, protons are accelerated from rest through a potential difference to a speed of approximately 3.1 x 10 6 meters per second. The resulting proton beam produces a current of 2 x 10-6 A. a. Determine the potential difference through which the protons were accelerated. b. The proton enters a region of uniform magnetic field B, as shown above, that causes the beam to follow a semicircular path. i. Determine the magnitude of the field that is required to cause an arc of radius 0.10 m. ii. What is the direction of the magnetic field relative to the axes shown above on the right?

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