Problem 2: Loop the Loop Consider the two digital TV loop antenna designs shown in Fig. 18.12. Both consist of two circles, both of radius a, lying in the xy-plane. In one case (A), the wires connecting the circle cross. In the other case (B), the wires do not cross. You may ignore the small gap between the leads going to and coming from the loop, and the deviation from an exact circular shape near the connection between the circles. An electromagnetic (EM) wave, propagating in air along the x-axis, has a magnetic field at the location of the antenna directed along the z-axis and is given by B(r) = B cos(wt)k. (18.82) (This requires that the wavelength of the EM wave is much larger than the radius of the antenna, which you should assume is the case here.). (a) What is the net magnetic flux, g, . through loop (A) as a function of B. 1, w, and a\" (b) What is the net magnetic flux, g , . through loop (B) as a function of B, t. w, and a\" Fig. 18.12 Loop antennae f (/\\ 3// D (c) What is the EME, V| 4,. generated around loop (A)? (d) What is the EMF, V|g,. generated around loop (B)? (e) Now, a resistor, R, is connected across the terminals of each loop. What is the current, /(4. around loop (A)? (f) What is the current, /;g). around loop (B)? What is the direction of the current in this case