Can the B field be obtained from the magnetic potential using matrix inversion?

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Discussion Overview

The discussion revolves around the relationship between the magnetic field (B field) and the magnetic vector potential (A field), specifically exploring methods to derive one from the other. It includes theoretical considerations and mathematical approaches related to electromagnetic fields.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant inquires about obtaining the B field from the magnetic potential, mentioning difficulties with matrix inversion.
  • Another participant states that the B field is derived from the curl of the vector potential, indicating uncertainty about the matrix approach.
  • A participant later reverses the question, asking how to obtain the A field from a given B field.
  • In response, a participant suggests that the method depends on the specific problem and refers to Green's functions for further guidance.
  • Another participant proposes a formula relating A and B fields, although they express some uncertainty about its accuracy.
  • A participant acknowledges the suggestion and notes that checking the formula could be done by calculating the curl.

Areas of Agreement / Disagreement

Participants express differing views on the methods for deriving the B field from the A field and vice versa. There is no consensus on the best approach or the validity of the proposed methods.

Contextual Notes

Some limitations include potential missing assumptions regarding the conditions under which the relationships hold, as well as the dependence on specific problem contexts and definitions of the fields.

Who May Find This Useful

This discussion may be of interest to students and professionals in electromagnetism, particularly those exploring the mathematical relationships between magnetic fields and potentials.

sinyud
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How do you get the B field from the magnetic potential?
I tried converting the curl into matrix format, but the corresponding matrix can't be inverted.
 
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It's just the curl of the vector potential:

[tex]\vec B = \nabla \times \vec A[/tex]

I'm not sure what you're tyring to do with it.
 
I got it backward. How do you the A field from a B field?
 
Oh! Well in that case ... it depends on what problem you're trying to solve. Check with a good E&M book for some discussion on Green's functions. That might help. It's been a while since I worked with that so I'd have to review it myself.
 
[tex]\vec{A} = \pm \frac{1}{2} \vec{B} \times \vec{r}[/tex] if memory serves me correctly...
 
Thanks, Dr. T! Sinyud could easily check that by calculating the curl.
 

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