1 A proton moving with a speed of 6.27 x 105 m/s in the positive y direction experiences zero magnetic force. When it moves in the negative z direction with the same speed of 6.27 x 105 m/s, it experiences a force of 1.65 x 10-13 N that points in the positive x direction. (a) (10) What are the direction and magnitude of the magnetic field? You may specify the direction of the net magnetic field either in terms of unit vectors, x-hat, y-hat or z-hat or as a vector drawn in the coordinate system below. (b) (5) Find the magnitude and direction of the electric field which would exert a force on the proton that would cancel out the magnetic force. xyz coordinate system.jpg Problem 2 One long, straight wire, which we shall call Wire A, carries a current of IA = 11.3 A. Wire A lies a distance d = 0.350 m to the left of a square loop with sides L = 1.50 m in length, as shown in the figure below. The loop carries a current of I = 4.52 A in the direction indicated. Another long, straight wire, which we shall call Wire B, carries a current of IB = 6.91 A. Wire B lies distance d = 0.350 m to the right of the square loop, as shown below. Find the magnitude and direction of the net force acting on the loop. 2 straight wires and square loop.jpg Problem 3 A conducting rod of mass m = 0.0592 kg is suspended from two vertical conducting springs separated by a distance L = 1.25 m. Assume the height of the conducting loop is also L = 1.25 m. The resistor shown at the top of the conducting loop has a resistance R = 10.2 . The entire system is immersed in a uniform magnetic field of magnitude B = 0.0592 T, as shown below. It is desired to reduced the tension in the springs to zero. (a) (8) What electric current would be required to pass through the conducting rod in order for the tension in both springs to be zero? Give both magnitude and direction (left or right) of the current. (b) (2) In order to establish a current in the direction desired in part (a), should the ambient magnetic field increase or decrease in strength? (c) (10) Find the magnitude of the required rate of change of the magnetic field that would bring about the required current found in part (a). rod hanging from 2 springs.jpg Problem 4 The circuit shown below consists of a 50.70-V battery, and inductor, two 32.5- resistors, and another resistor of unknown resistance, R. After the switch in the figure below has been closed for a long time, the current in the inductor is 1.25 A. Suppose the inductor is a solenoid which has 259 turns, a circular cross section of radius 0.0522 m, and a length of 54.2 cm. (a) (3) Find the inductance L of the inductor. (b) (10) Find the value of the resistance, R. (c) (3) Find the energy stored in the inductor a long time after the switch is closed. (d) (9) Find the time, t, required for the current in the battery to increase from 0 to 0.981 A. LR Circuit.jpg Problem 5 The reflecting surfaces of three mirrors form vertices with angles of 163o and 124o, as shown in the figure below. A ray of light strikes mirror 1 with an angle of 33.2o with the surface of mirror 1. Find the angle of reflection 3r when the ray leaves mirror 3