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spring_07_exam4_phy2054

# spring_07_exam4_phy2054 - PHY2054 Spring 2007 Prof Eugene...

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PHY2054 Spring 2007 1 Prof. Eugene Dunnam Prof. Paul Avery Apr. 28, 2007 Exam 4 Solutions 1. A charge of 5 microC is placed at the origin and a +10 microC charge is located at x = 1.0 m. Where, on the x-axis, is the net electrostatic field equal to zero, and is the electrostatic poten- tial at this point also zero? (1) x = +2.41 m; no (2) x = 2.41 m; no (3) x = +1.00 m; yes (4) x = 0.62 m; no (5) none of these The electric field must be zero for points to the right of the smaller charge (x > 0) because in that region the field from the larger charge is compensated by the greater distance. If +2q is the charge at x = 1.0 and q is the charge at the origin, then the equation for E x = 0 can be written ( ) 2 2 / 2 / 1 0 kq x kq x + + = . Solving yields 2 1 2.41 x = + + ± m. 2. The sketch depicts a 50-turn rectangular loop of dimensions a = 55 cm and b = 130 cm, and rotated by an angle θ = 65 ° from the y axis. It is hinged along the z axis and immersed in a uni- form magnetic field B = 0.27 T pointing in the + z direction. The current in the loop is 4.5 A. The torque on the loop (in N m) and its direction of rotation, viewed from above, is (CW = clockwise and CCW = counterclockwise) (1) 0.0 (2) 0.79, CW (3) 0.37, CCW (4) 0.87, CW (5) 2.92, CCW Only the currents along the top and bottom of the loop contribute to the torque since the currents on the side generate zero force apiece. However, the torques from the top and bottom parts of the loop cancel because the forces are equal and opposite and the lever arm is the same. x z y ± a b B

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