At t=0, a rectangular coil of resistance R = 2 ohms and dimensions w = 3 cm and

Question

At t=0, a rectangular coil of resistance R = 2 ohms and dimensions w = 3 cm and L = 8 cm enters a region of constant magnetic field B = 1.6 T directed into the screen as shown. The length of the region containing the magnetic field is LB= 15 cm. The coil is observed to move at constant velocity v = 5 cm/s. What is the force required at time t = 0.8 sec to maintain this velocity? F(0.8 sec)

At t=0, a rectangular coil of resistance R = 2 Ohms and dimensions w = 3 cm and L = 8 cm enters a region of constant magnetic field B = 1.6 T directed into the screen as shown. The length of the region containing the magnetic field is LB=15cm. The coil is observed to move at constant velocity v = 5 cm/s. What is the force required at time t = 0.8 sec to maintain this velocity? F(0.8 sec)

Explanation / Answer

Given data Resistance, R = 2 ? Width of the region of constant magnetic field is, w = 3 cm = (3 cm) (0.01 m / 1cm) = 0.03 m Magnetic field, B = 1.6 T Velocity of the coil is, v = 5 cm /s = ( 5 cm ) (0.01 m / 1cm) / s = 0.05 m /s Solution: A rectangular loop is held in a uniform magnetic field B and isin the plane of the paper. The magnetic field is perpendicular to the plane of the paper and is directed inward. The loop is moves towards right in theplane of the paper and perepndicular to the field with a constant velocity v. The force required to maintain this velocity can be obtained as, The induced emf is, e = B w v And induced current, I = e / R = B W v / R Now, force F = I w B = (B w v / R ) w B = B2w2v / R = (1.6 T )2 (0.03 m)2 (0.05 m/s) / 2 ? = 5.76 * 10-5 N Given data Resistance, R = 2 ? Width of the region of constant magnetic field is, w = 3 cm = (3 cm) (0.01 m / 1cm) = 0.03 m Magnetic field, B = 1.6 T Velocity of the coil is, v = 5 cm /s = ( 5 cm ) (0.01 m / 1cm) / s = 0.05 m /s Solution: A rectangular loop is held in a uniform magnetic field B and isin the plane of the paper. The magnetic field is perpendicular to the plane of the paper and is directed inward. The loop is moves towards right in theplane of the paper and perepndicular to the field with a constant velocity v. The force required to maintain this velocity can be obtained as, The induced emf is, e = B w v And induced current, I = e / R = B W v / R Now, force F = I w B = (B w v / R ) w B = B2w2v / R = (1.6 T )2 (0.03 m)2 (0.05 m/s) / 2 ? = 5.76 * 10-5 N A rectangular loop is held in a uniform magnetic field B and isin the plane of the paper. The magnetic field is perpendicular to the plane of the paper and is directed inward. The loop is moves towards right in theplane of the paper and perepndicular to the field with a constant velocity v. The force required to maintain this velocity can be obtained as, The induced emf is, e = B w v And induced current, I = e / R = B W v / R Now, force F = I w B = (B w v / R ) w B = B2w2v / R = (1.6 T )2 (0.03 m)2 (0.05 m/s) / 2 ? = 5.76 * 10-5 N

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