Using Ampere's Law to Calculate Magnetic Field at a Point

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Discussion Overview

The discussion revolves around the application of Ampere's Law to calculate the magnetic field at a specific point, particularly in scenarios where the conditions for using the law may not be straightforward. Participants explore theoretical approaches and alternative methods for determining the magnetic field.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the feasibility of using Ampere's Law to calculate the magnetic field at a single point without a suitable surface where the magnetic field is constant.
  • Another participant suggests that Ampere's Law at a point relates to the Maxwell equation for curl B and implies that a differential equation must be solved for the magnetic field.
  • A participant seeks clarification on the notation B~j, which appears to be a point of confusion.
  • It is proposed that depending on the specific setup, the Biot-Savart law might be a more appropriate method to use instead of Ampere's Law, with a note on the potential difficulty in expressing current density J.
  • Further clarification on the notation is provided, indicating that the curl of B is proportional to the current density j, with a mention of unit system variations affecting the constant of proportionality.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Ampere's Law in this context, with some suggesting alternative approaches like the Biot-Savart law. The discussion remains unresolved regarding the best method to calculate the magnetic field at a point.

Contextual Notes

There are limitations regarding the assumptions made about the magnetic field's behavior and the specific configurations of current that may affect the applicability of the discussed laws.

swraman
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Is there any way to use Ampere's Law [tex]\oint_{C}\beta d\ell = \mu_{0}I[/tex] to calculate the magnetic field [tex]\beta[/tex] at a single point if there are no surfaces C such that [tex]\beta[/tex] is constant over the surface's perimeter?

Thanks

Raman

Edit: I mean solve symbolically, no estimation/splitting the integral up into discrete sums
 
Last edited:
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Ampere's law at a point is the Maxwell equation for curl B~j.
You then have to solve a differential equation for B.
 
what is B~j?
 
Depending on the set-up, you may be better off using the Biot-Savart law instead. There may or may not be a way to get an expression for current density J depending on how the question is given.
 
swraman said:
what is B~j?
Maxwell's equation is (Curl B)=k j. The constant k is different in different systems of units.
By ~ I meant that (Curl B) was proportional to j.
 
Oh ok Thanks
 

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