Radiation from a Square Loop of Current

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Discussion Overview

The discussion centers on whether a square loop of steady current radiates electromagnetic energy, drawing comparisons to the well-known behavior of circular loops. Participants explore the conditions under which radiation occurs, particularly focusing on the nature of the current and the motion of charges within the loop.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant states that a circular loop of steady current does not radiate, raising the question of whether a square loop behaves similarly.
  • Another participant argues that for radiation to occur, the electric field lines must have a transverse component, which only arises if the current is varied, such as in AC circuits or during switch-on events.
  • It is noted that radiation occurs when there is a changing dipole moment or higher moments, implying that steady currents do not radiate.
  • A participant mentions the possibility of cyclotron radiation if electrons move fast enough, suggesting that in typical wires, the slow speed of electrons (e.g., 1 mm per hour) does not lead to significant radiation, unlike in vacuum tubes where electrons can move much faster.
  • Another participant speculates that the radiated power could be described by Larmor's formula, referencing the radial acceleration of charges.
  • A later reply confirms the use of Larmor's formula in the context of radial acceleration.

Areas of Agreement / Disagreement

Participants generally disagree on whether a square loop of steady current radiates, with some asserting that it does not while others introduce conditions under which radiation might occur, such as varying currents or fast-moving electrons.

Contextual Notes

The discussion includes assumptions about the nature of current, the behavior of electric fields, and the conditions necessary for radiation, which remain unresolved and dependent on specific definitions and contexts.

STosh9
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It is well known that a circular loop of steady current does not radiate, even though each individual charge is undergoing centripetal acceleration.

How about a loop of steady current that is shaped in a square? Does this structure radiate?
 
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How about a loop of steady current that is shaped in a square? Does this structure radiate?
Imagine the static field of the charges in the wire. The lines of force point radially outwards everywhere, and are always normal to the wire. Even when it goes round a corner they are normal to the wire. To have radiation, they need to be not normal but pushed to one side a bit. In this way a transverse component of field is created, the radiated E-field. This only occurs if the current is varied, as with AC or at switch-on.
 
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You get radiation when you have a changing dipole (or higher) moment. So nothing with a steady current will radiate.
 
Further to my reply, if the electrons can move fast enough with a steady current it is possible to obtain cyclotron radiation. But electrons in a wire are only traveling at, say, 1 mm an hour. In a vacuum tube it is possible for them to go round millions of times a second, and then cyclotron radiation can be seen at the rotation frequency.
 
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tech99 said:
Further to my reply, if the electrons can move fast enough with a steady current it is possible to obtain cyclotron radiation. But electrons in a wire are only traveling at, say, 1 mm an hour. In a vacuum tube it is possible for them to go round millions of times a second, and then cyclotron radiation can be seen at the rotation frequency.
and i guess radiated power will be given by Larmor's formula ?
 
debajyoti datta said:
and i guess radiated power will be given by Larmor's formula ?
Yes, taking the radial acceleration.
 

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