Electromagnetism: Please, how to solve the problem in detail?
1. Rotating magnetic dipole: We have a along the z-axis. We have a circular coil of radius R on x-y plane. There is a constant current lo passing through the coil counter-clockwise direction when it is seen from the positive z-axis.
a. What is the magnetic moment mo of this coil?
b. What is the magnetic vector potential A by the magnetic dipole mo at the origin?
c. What is the expression for the magnetic vector potential A when mo oscillates with mot= mocos?
d. Calculate the electric and the magnetic fields E, Ho from A when the distance r of the observation point from the origin is much greater than R.
e. What is the Poynting vector Sort in the far field?
f. What is the time-averaged Poynting vector S=Sot?
g. What is the time-averaged energy flux out of a sphere whose radius is r in the far field?
Let's consider a different case when the magnetic moment mo is rotating along the y-axis with an angular frequency, such that mt=mo[2cost+sint]=mot+mt.
h. What are the electric and the magnetic fields Et, Ht generated by the second magnetic dipole given as mt=mgsint?
i. What are the total electric and magnetic fields Et=Eo,t+Et,H,t=Hft+ Hrtof the rotating dipole?
j. What is the total Poynting vector S,t=Sort+Sr,t of the rotating dipole?
k. What is the time-average of the total Poynting vector Sr=St?
l. What is the total time-averaged energy flux out of a sphere whose radius is r in the far field?