A 50-turn square coil with a cross-sectional area of 3.00 cm^2 has a resistance

Question

A 50-turn square coil with a cross-sectional area of 3.00 cm^2 has a resistance of 18.0 Ohm. The plane of the coil is perpendicular to a uniform magnetic field of 1.00 T. The coil is suddenly rotated about the axis shown in the figure below through an angle of 60 degree over a period of 0.200 s. What charge flows past a point in the coil during that time? If the loop is rotated a full 360 degree around the axis, how much total charge passes the point in the loop? A 50-turn square coil of wire has a cross-sectional area A = 3.00 cm^2 and a resistance R = 18.0 Ohm. The plane of the coil is initially perpendicular to a uniform magnetic field of magnitude B = 1.00 T. The coil is suddenly rotated through an angle of 60 degrees in a time period of 0.200 s. Even though the magnetic field and the cross-sectional area remain constant, the angle between the magnetic field vector and the area vector changes. This means a potential, and therefore a current, will be induced in the coil. By combining Faraday's law and Ohm's law, we can calculate the total charge that flows past a point in the coil while the loop is rotated. If the loop is rotated a full 360 degrees, we would expect the net charge passing a given point in the loop to be zero.

Explanation / Answer

change in flux throgh the loop

dphi = N*B*A*(1 - cos60)

emf induced e = dphi/dt = (50*1*3*10^-4*(1-cos60))/0.2 = 0.0375 V

current i = e/R

charge = i*dt = (0.0375*0.2)/18 = 4.17*10^-4 A

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