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Consider a long solenoid (I = 12 cm in length) that has N = 100 turns and a radius R = 1 cm. Inside of this solenoid is a metal ring with a total resistance of 10 and a radius of r = 0.75cm; this ring is placed in the center of the solenoid, as shown in the diagram below. A current is applied to the solenoid which has the following form $1(t) = 2.5A.cos(41) Osts 0.25s t> 0.25s (1070) = -2.5A The coil is wound such that at = = 0, the magnetic field points to the left. The direction the current is flowing through in the solenoid at this time is indicated on the diagram. N-turns Current(A) Blto) $18.XIDO 2 R 1 0.05 0.10 2.15 Time(s) 0.30 0.20 0.25 000 -2 g ) a.) What is the expression for the magnetic flux, Pm, through the small ring at some timet? b.) At what time is the induced emf in the ring at its maximum? Explain? c) What is the magnitude and direction of the current induced in the ring by the solenoid's magnetic field at time 1 = 0.125s? d) What is the current induced in the ring at time t = 0.3s? Explain your answer. e.) What is the total magnetic field strength in the center of the ring at time + = 0.05s? (Hintis this field just from the solenoid?)