?A uniform magnetic field, B = 1.2 T, points out of the page perpendicular to th

Question

?A uniform magnetic field, B = 1.2 T, points out of the page perpendicular to the loop. A conducting loop is made from two parallel conducting rails connected by a 2.4-volt battery and a 12 ? resistor. The loop is completed by a conducting bar, which can slide without friction along the rails. The bar, which can slide either left or right, has a length L = 0.50 m. The width of the loop is initially 4.0 m. Assume the rails and rod have negligible resistance, and that the rails extend a long way both left and right out of the picture above. If the rod slides to the left, it can pass over the resistor and battery without hitting them.

a) After a very long time, the rod is observed to be moving at constant velocity. What is the current in the circuit when this happens?

b) After a very long time, what is the speed of the rod?

c) Return to the original initial condition of v = 0 at t = 0. The magnetic field is now changed so as to keep the net force on the rod zero. What is the rate of change of magnetic field, ?Bt , required to ensure that the net force on the rod is zero? Indicate the magnitude of ?Bt and whether B needs to increase or decrease in magnitude.

Explanation / Answer

a) I = V/(r) = 2.4/(12) = 0.2 A
b) Direction -> Towards right
magnitude = BIL = 1.2*0.2*0.5 = 0.12 N
c) rate of change of area of loop = 0.5*v
rate of change of phi = 0.5*v*1.2 = 0.6v
net emf = 2.4-0.6v
net I = (2.4-0.6v)/12
net F = 0.6*(2.4-0.6v)/12 = 0.05(2.4-0.6v) = 0
v = 4 m/s
  I = 0

c) ftime rate of flux should be 2.4 V
flux at time t DB*A
time rate = Db*A/dt = 2.4
so, Db*w*vt/dt = 2.4
so, Dbt = 2.4*dt/w
it needs to increase (positive dphi) to indue negative emf to counter the battery

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