Magnetic field of a rectangular coil

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Discussion Overview

The discussion revolves around the formula for the magnetic field generated by a rectangular (specifically square) coil. Participants explore the derivation of the formula, its components, and the challenges faced in understanding it, particularly in relation to integration techniques.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant presents a formula for the magnetic field at the center of a square coil and expresses confusion about its derivation and the factor of 2 involved.
  • Another participant clarifies that the formula is derived using the Biot-Savart law and explains the integration process for a wire segment, noting the specific limits used for a finite wire segment.
  • A different participant seeks a method to avoid integrals, drawing parallels between the square coil and the formula for a single wire segment, but acknowledges difficulties in reconciling the two approaches.
  • One participant suggests that understanding square loops may require knowledge of integration, implying that the current level of understanding may be insufficient for the topic.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the derivation of the magnetic field formula, with some confusion about specific factors and the necessity of integration. No consensus is reached on the best approach to understand the topic without using integrals.

Contextual Notes

Participants indicate limitations in their current knowledge, particularly regarding integration techniques, which may affect their ability to fully grasp the derivation of the magnetic field formula.

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I got this formula for the magnetic field of a square-shaped coil: B = m0*2*sqrt(2)*I*N/(a*pi), where m0 is the permeability, and a is the side of the square... I can't really get why it is so, and my best tries resulted in approximation of the 'diameter' of the coil, for example by taking the diagonal of the square... thanks in advance!
 
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That formula is for the field at the center of the square, although I don't get the factor of 2. It is derived by using the Biot-Savart law for a wire segment of length a four times.
The field of a wire segment of length a is found by integrating from -a/2 to +a/2, instead of infinity in the usual derivation for an infinite wire.
 
hm, is there a way to avoid integrals? i found some similarities with the formula for a single wire segment, B = m0*I/(2*r*pi), as a single loop is just 4 of these put in shape of a square, and the orientation of the vector for every segment is the same if we look at the magnetic field in the center, but this turns out to be just four times the formula given above, and r = a/2, so i get B = 4*m0*I/(r*pi)

//edit
ok, i read the 'instead of infinity' now... i guess no hope for getting it right, i guess, as we haven't done integrals yet in school
 
Last edited:
You'd better hold off on square loops until integration.
 

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