Problem 3345 The square loop shown in the figure moves into

Problem 33.45 The square loop shown in the figure moves into a 0.80 T magnetic field at a constant speed of 10 m/s. The loop has a resistance of 0.10 , and it enters the field at t =0s. 10 cm 10 cm B-0.80 T Part A Find the induced current in the loop as a function of time. Give your answer as a graph of I versus t fromt 0stot 0.020 s. Plot 1 for the whole time interval from t = 0 s to t 0.020 s . This content is not avalable on your mobile device, but your work isn solution for grading Pease use adivent device to submg your Part B What is the maximum current? Express your answer to two significant figures and include the appropriate units. 1Value Units Submit My Answers Give Up Part C What is the position of the loop when the current is maximum? OThe maximum current is when the loop is at the end of the region of the field. O The maximum current is when the loop is halfway into the region of the field o The maximum current is when the loop is at the beginning of the region of the field. Submit My Answers Give Up

Solution

A(t) = 2 (1/2 x²) = x² = v² t²

dA / dt = 2 v² t = 0

d I_B / dt = dA / dt * B

= 2 v² t * B = 2 * 10² * t * 0.80 = 160 t

I = V / R = 160 t / 0.1 = 1600 t

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position = 10 / / sqrt [2]

t = 7.07 ms

I = 1600 t = 1600 * 7.07 * 10^-3

= 11.3 A

the maximum current is when the loop is halfway into region of field