Current loops and electric dipoles

[amir11]

Hello Physics enthusiasts

Imagine an infinitesimal small current loop where the current can run clockwise or counterclockwise at frequency v. I am trying to find a linear combination of the two(current loops) which creates the same electric field pattern (far from the dipole) as a very small current running on a very small line(electric dipole).

In principle it should be possible but I am not sure how to tackle the problem. Could you please help me with this?

 

[Dale]

Hello Physics enthusiasts

Imagine an infinitesimal small current loop where the current can run clockwise or counterclockwise at frequency v. I am trying to find a linear combination of the two(current loops) which creates the same electric field pattern (far from the dipole) as a very small current running on a very small line(electric dipole).

In principle it should be possible but I am not sure how to tackle the problem. Could you please help me with this?

I suspect that it is not possible in principle. A small current loop gives a magnetic dipole field, so two loops in general gives a magnetic quadrupole field. I don't know any reason to believe that a magnetic quadrupole should give an electric dipole.

 

[UltrafastPED]

This note on moving electric dipoles may help with the mathematical techniques:
http://www.physics.princeton.edu/~mcdonald/examples/movingdipole.pdf

 

[Meir Achuz]

Equal clockwise and anti-clockwise currents in a loop of radius R, oscillating at an angular frequency
w=c/R would be equivalent to an electric dipole.

 

[Dale]

Are you sure of that? It would surprise me.

 

[amir11]

I also think that it shuld be just a linear combinition of the two right and left propagating currents that give the solution but I can't derive it mathematically. Any suggestion?

 

[amir11]

Consider a straight wire of Length L. Let an oscillating current of wave length L/2 enter the wire at one end.
This is an electric dipole. Place two such wires side by side, each with the same current. This is still an electric dipole. Now pull the wires apart from their centers to form two semicircles. Isn't this still an elctric dipole?

Thanks for the reply. It is an electromagnetic source of energy, but this dose not mean that it behaves the same way as a dipole, neither it means that a combination of clock and counterclockwise current loops will give a linear dipole. I am kind of looking for a solid mathematical argument.

 

[Dale]

Consider a straight wire of Length L. Let an oscillating current of wave length L/2 enter the wire at one end.
This is an electric dipole. Place two such wires side by side, each with the same current. This is still an electric dipole. Now pull the wires apart from their centers to form two semicircles. Isn't this still an elctric dipole?

I would think that it would be at least quadrupole, but my "multipole kung-fu" is admittedly weak

 

[Spinnor]

Equal clockwise and anti-clockwise currents in a loop of radius R, oscillating at an angular frequency
w=c/R would be equivalent to an electric dipole.

Are the currents nearly superimposed? If so the net current is zero, you got nothing? What am I missing?

 

[Spinnor]

Hello Physics enthusiasts

Imagine an infinitesimal small current loop where the current can run clockwise or counterclockwise at frequency v. I am trying to find a linear combination of the two(current loops) which creates the same electric field pattern (far from the dipole) as a very small current running on a very small line(electric dipole).

In principle it should be possible but I am not sure how to tackle the problem. Could you please help me with this?

A general alternating current is the sum of a part that has a divergence and a part that has a curl? Don't those different alternating currents give rise to fundamentally different radiation fields?

 

[Meir Achuz]

I'm sorry. My previous posts were wrong. Please forget them,