Please answer all parts SHOWING ALL STEPS CLEARLY EXPLAINING THE CONCEPTS!! Also, please make sure all solutions are 100% correct. DO NOT USE CALCULUS (Integration, Cross product, etc.) TO SOLVE ANY OF THESE QUESTIONS. Thank you very much!

. A moveable (massless and frictionless) conducting rod with a length of L = 0.5 ' ' ' ' ' ' ' meters is being moved at a constant speed along two conducting rails by a constant external force, as shown in the gure. The entire system is immersed in a uniform constant 3 T magnetic eld (out of the paper). If the resistance R = 49 and the power dissipated in the resistor is 256 Watts, What is the magnitude of the external force Fext (in N)? (1) 12 (2)3 (3) 6 (4) 9 (5) 15 . What is the induced emf in the previous problem (in Volts)? (1) 32 (2) 8 (3) 16 (4) 4 (5) 24 Consider the LR circuit shown in the gure which consists of an 8 Volt emf, an inductor, L = 4 H, and two resistors. After the switch is closed, what is the l stored energy in the inductor (in J) at the instant the current through the 2 Q resistor is equal to 3 A? _8V 122:4 n (1) 40.5 (2) 4.5 (3) 18.0 (4) 72.0 (5) 2.0 Consider the LR circuit shown in the gure. Initially the inductor has no magnetic stored energy and the switch is closed at t = 0. Immediately after I the switch is closed the current through the 29 resistor is Ishort and a long _ 8Q time after the switch is closed (3162., steady state) the current is Long. What is 8 the ratio I long / Ishort? 2 Q (1) 5 (2) 3 (3) 4 (4) 1/3 (5) 1/5 Consider the two circular current loops with centers at the origin (x = y = z = 0) shown in the gure. The smaller loop has radius 7', carries current I, and lies in the yz-plane. The larger loop has radius 27', carries a current 21 , and lies in the xyplane. If r = 0.5 In and I = 3 A, what is the magnitude of the net magnetic eld (in MT) at the origin due to the two current loops? (1) 5.33 (2) 1.78 (3) 3.55 (4) 7.54 (5) zero What electric field strength (in kV/m) has the same energy density (in J/m3) as does a 5/T magnetic field? (1) 1.5 (2) 1.2 (3) 1.8 (4) 1.0 (5) 2.0