A metal bar able to move on fixed rails is initially at rest on two stationary c
ID: 1832483 • Letter: A
Question
A metal bar able to move on fixed rails is initially at rest on two stationary conducting rails that are l = 50 cm apart and connected to each other via a Vo = 10 V in series with a R = 10ohm resistor. A constant magnetic field of Bo = z^ 1.5 T is turned on at t=0. Assume the rails and the metal bar to be perfectly conducting, and neglect the selfinductance of the loop formed by the rails and the bar. The initial resting position of the bar is at yo = 75 cm. Assuming the mass of the bar is .5 kg and no friction a) calculate the magnitudes and directions of its initial acceleration and its final velocity. b) Describe what happens if the voltage source is turned off(i.e., Vo =0) at t=to, when the bar has reached a velocity vo. c) what happens if the voltage source remains at Vo but the magnetic field is turned off.
Any help is greatly appreciated. Thanks!
Explanation / Answer
The expression that you have written for the magnitude of the magnetic field doesn't seems to be correct so am deriving the expression which you can substitute with the proper value of B and find the first part. a) Current flowing through the bar and in the circuit = V/R = 10/10 = 1 amps. We know that force on a conducting wire in a magnetic field is equal to F = i ( lxB) where x is the cross product. using the right hand thumb rule the force come out to be directed in the positive y direction( with reference to the coordinated mentioned in the question). so the magnitude of the force = 1(.5*B) = B/2 Newtons and the magnitude of acceleration (A)= F/m = B/(2*.5) = B m/sec^2. Now the final velocity of the bar can be calculated considering the net forces on the bar. Due to moving of the rod the loop also induces an emf which tries to oppose the force experienced by it. Therefore the rod attains a constant velocity which is given by the relation. B*v*l = i * l *B or v = 1 m/s since i =1 amps and B and l are common both sides. b) when the voltage source is turned off the force due to changing flux takes over and the bar comes to a rest after a while as induced emf produces a force opposite to the direction of motion. These forces can be calculated from right hand thumb rule. c)Essentially nothing happens and the rod continues to move with the velocity attained during the part a. Hope you understand. If you have any query further do feel free to ask. b)