Problem 101-2    Source:   Adapted from example 1-10 - page 43 - CHAPMAN, Stephen J. -    Book: Fundamentals of Electric Machines - 5th edition - Ed. McGrawHill - 2013.

Considering the previous problem (Problem 101-1), find:

a) The steady-state speed if a force of 30 N pointing to the left were applied to the bar. Would this machine be a motor or a generator?

b) Assume that the bar is unloaded and that it suddenly enters a region where the magnetic field is weakened having the value of 0.08 T. How fast is the bar? will it move?

Solution of the Problem 101-2   

Item a

Since the applied force is pointing to the left then the induced force points to the right. And since we are in steady state, the two forces have the same intensity and is given by eq. 101-01, reproduced below for clarity.

Doing a little algebraic work on this equation, we get:

Now, using the eq. 102-06 and after some algebraic work, we find:

Naturally, this machine operates as a motor transforming the electrical energy from the source into mechanical energy of movement from the bar.

Item b

If the bar is initially uncharged, we know that ε_ind = V = 120 volts. If the rod suddenly hits a region of weaker magnetic field, a transient will occur. After the transient, the bar enters steady state and, again, we will obtain the situation of ε_ind = V. Using this fact we can determine the velocity of the bar using the eq. 101-06 with the algebra from the previous item. So: