Determining the Poynting Vector for Loop Antennas

[Mat1289]

So I came across the following image (from Wikipedia)

where the electric and magnetic field lines are depicted for a dipole antenna. From the field lines, it is possible to determine the direction of the poynting vector, using the right-hand rule. If all possible combinations of poynting vectors are considered, an entire plane is described, perpendicular to the antenna axis.

I was wondering if there is an analogous consideration for loop antennas. I came up with the following sketch

whereby the loop is situated in the XY plane. I drew in one possible electric and magnetic field line for a certain time instance. If the "A" is considered and the right-hand rule is applied, the poynting vector lies on the X-axis. If however point "B" is considered, the magnetic field and electric field are opposite to each other and the poynting vector can't be resolved.

1) Is my assumption of the field lines possible/correct?
2) How to determine the poynting vector in the case of the loop antenna?
3) How about near/far field effects; under which circumstances are such considerations valid? Is the dipole an exceptional example that "always" works?

Constructive and elaborated answers are appreciated.

 

[tech99]

So I came across the following image (from Wikipedia)

where the electric and magnetic field lines are depicted for a dipole antenna. From the field lines, it is possible to determine the direction of the poynting vector, using the right-hand rule. If all possible combinations of poynting vectors are considered, an entire plane is described, perpendicular to the antenna axis.

I was wondering if there is an analogous consideration for loop antennas. I came up with the following sketch

whereby the loop is situated in the XY plane. I drew in one possible electric and magnetic field line for a certain time instance. If the "A" is considered and the right-hand rule is applied, the poynting vector lies on the X-axis. If however point "B" is considered, the magnetic field and electric field are opposite to each other and the poynting vector can't be resolved.

1) Is my assumption of the field lines possible/correct?
2) How to determine the poynting vector in the case of the loop antenna?
3) How about near/far field effects; under which circumstances are such considerations valid? Is the dipole an exceptional example that "always" works?

Constructive and elaborated answers are appreciated.

(My views on this do not meet with universal agreement).
For both antennas, radiation is caused by the acceleration of charges. This is the case for any antenna, whatever the shape, including slots and loops.
Now think of a square loop.
For this loop antenna, each side of the loop is just a wire, and radiates the same as a dipole.
The two wires create a figure-of-eight radiation pattern when viewed at a long distance, due to phase cancellation. There is zero radiation broadside to the loop and maximum in the plane of the loop.
Do not be confused by the induction fields of the two types of antennas, which are just local energy stores and not germane to radiation.

 

[Baluncore]

The poynting vector shows the direction of energy flow. Since the antenna radiates, the poynting vectors will be diverging outwards like pins in a pin cushion. Since the poynting vectors branch and get thinner it is not possible to draw them as continuous line or plane.