# Current loops and electric dipoles

• amir11
In summary, it is not possible to create an electric field that is the same as a very small current running on a very small line.
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?

amir11 said:
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.

1 person
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.

1 person
Are you sure of that? It would surprise me.

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?

Meir Achuz said:
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.

Meir Achuz said:
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

Meir Achuz said:
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?

amir11 said:
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?

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

## 1. What is a current loop?

A current loop is a closed path or circuit through which an electric current flows. It can be in the form of a wire loop or a coil of wire. The direction of the current flow in a current loop is typically represented by using a right-hand rule.

## 2. How is a magnetic field produced by a current loop?

A current loop produces a magnetic field around it due to the flow of electric charges. The direction of the magnetic field can be determined by using the right-hand rule. The strength of the magnetic field is directly proportional to the current flowing through the loop and the number of turns in the loop.

## 3. What is an electric dipole?

An electric dipole is a pair of equal and opposite charges separated by a small distance. This creates a dipole moment, which is a vector quantity that describes the separation and magnitude of the charges. Electric dipoles can be found in molecules and atoms, and they experience torque when placed in an electric field.

## 4. How are electric dipoles related to current loops?

A current loop can be thought of as a collection of many tiny electric dipoles, with each loop contributing to the overall magnetic field. When a magnetic field is applied to a current loop, the loop experiences a torque, similar to how an electric dipole experiences a torque in an electric field.

## 5. What are some practical applications of current loops and electric dipoles?

Current loops and electric dipoles have various applications in fields such as electromagnetism, electronics, and medical imaging. They are used in devices such as electric motors, generators, MRI machines, and antennas. They are also important in understanding the behavior of electromagnetic waves and the interaction between electricity and magnetism.

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