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PHYS-222 Worksheet 10 for Section 25 & 36 TA: Yang Li, leeyoung@iastate.edu October 15, 2012 Problem 10-1 In Fig. (a) and (b), what are the directions of the induced current repectively in the loop? (assume we look below at the loops) A. CCW, CCW B. CCW, CW C. CW, CCW D. CW, CW Problem 10-2 A railgun (See the figure below) comprises a pair of parallel conducting rails, along which a sliding metallic armature is accelerated by the electromagnetic field generated by the current carried on the rails . For simplicity, suppose the armature can be modeled by a metallic bar with length d. We further assume the magnetic field is uniform and proportional to the current I, B = k0 I. The effective resistance of the railway plus the armature is R. The length of the railway is L. The voltage between two rails is V . a. If at one time instant, the speed of the armature is v, what is the current I? Express your answer in V terms of v, V, R, d, L, k0 . I = R+k 0 dv b. What is its acceleration a? Express your answer in terms of v, V, R, d, L, k0 . a = V 2 k0 d m(R+k0 dv)2 c∗ . With the relation between a and v, calculate the final velocity vf of the armature. vf ' R k0 d , 2 2P0 τ 1 2 2 mv0 14 v0 where v0 = P0 = V /R, τ = L/v0 , assumming vf v0 . The meaning of v0 is the speed when the resistance voltage equals the magnetic induction emf. d∗ . Suppose the radius of the rails are a. Calculate k0 in terms of a, d, µ0 . k0 = µ0 ln(d/a−1) 2πd Figure 1: A railgun is an projectile launcher powered by electromagnetic field 1