At t = 0, a rectangular coil of resistance R = 2 ? and dimensions W = 3 cm and L
ID: 2141852 • Letter: A
Question
At t = 0, a rectangular coil of resistance R = 2 ? 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 ? 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?Explanation / Answer
I guess the "force" is required because electrical power is being dissipated
at a rate P = V^2 / R
Thus F (5 cm/s) = V^2 / (2.2 ohms)
The induced emf (V) is d(phi-B)/dt
the rate at which the coil's motion is increasing the magnetic flux through the coil.
At t = 0.8 seconds, the coil has partly entered the field, but is adding magnetic flux at a rate
B dA/dt = (1.8 T)(0.03 m)(0.05 m/s) = 2.7 x 10^(-3) T m^2/s = 2.7 mV
F (0.05 m/s) = (2.7 mV)^2 / (2.2 ohms) = 3.316 microwatts
F = 66 micronewtons
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