Problem 1. (20 points) Wireless transmission system
A circular wire loop carrying an alternating current I(t)=I0sin(2?ft) lies flat in the x-y planecentered at the origin (radius of the loop r=1.0 m, current amplitude I0=1.0 A, cycle frequencyf=60 Hz).
(A) Find the magnetic field B(t) at the center of the loop and express it as a function of time.
A smaller circular loop with radius a=0.01 m is placed at the origin parallel to the big loop. Theresistance of the small loop is R=5.0 Ohms.
(B) What is the magnetic flux passing through the small loop as a function of time?
(C) Find the emf induced in the small loop and express it as a function of time.
(D) Find the current in the small loop as a function of time. What is the ratio of the peak current in the small loop to the peak current in the big loop? Which of the quantitiesgiven in this problem does the ratio depend on?
(E) Make a diagram showing the currents in both the big (“transmitter”) loop and small(“receiver”) loop versus time on the same graph.