A rectangular loop of length 2a and width s is positioned such that the plane of the loop makes an angle ̠ with respect to the Z-axis, as shown in Figure 1. The loop is exposed to a magnetic flux density B varying as a function of time:
B = {
zB0 (t/t0) , 0 <= t < t0
zB0 (2 - t/t0) , t0 <= t < 2t0
}
a. [5 marks] Find the expression for the magnetic flux through the loop. Use the direction of dl in the sketch to determine if the flux is positive or negative.
b. [5 marks] Find the expression for electromotive force induced in the loop.
c. [5 marks] The electromotive force induces a current in the loop. What is the direction of this current for 0 <= t < t0? Indicate the current direction using a sketch in XY plane, similar to the Figure 1, showing the front view of the rectangular loop. State which law you used to determine the current direction.
d. [5 marks] The magnetic flux density is also the source for a torque acting on the loop. Determine the direction of the induced torque for the increasing B, 0 <= t < t0. Show the vector of the magnetic force acting on the loop using a sketch in XZ plane (the side view).
e. [5 marks] We now make the magnetic flux density invariant with time such that B = zB0. The loop is then made to rotate around Y-axis such that ̠ = wt. Calculate the electromotive force induced in the loop.
Figure 1. A rectangular loop of length 2a and width s placed in magnetic field. XZ plane shows the side view (left), XY plane shows the front view (right).