Ampere's law for a larger diameter?

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Discussion Overview

The discussion revolves around the application of Ampere's law in the context of conductive wires with larger diameters, particularly focusing on whether current density ##J## should be used instead of total current ##I## for calculating the magnetic field at points outside the wire. The conversation also touches on the implications of wire geometry on the Lorentz force.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question whether current density ##J## should be used for calculating the magnetic field at points ##r > R## for larger diameter wires, as opposed to using total current ##I##.
  • One participant suggests that if the current density ##J## is distributed with cylindrical symmetry, the total current ##I## can be used to calculate the magnetic field outside the wire.
  • Another participant argues that if the wire carries DC, it is intuitive to assume that the current is uniformly distributed, thus supporting the use of total current ##I##.
  • Some participants express uncertainty about when to apply current density ##J## in the context of magnetic fields and the Lorentz force.
  • One participant mentions experiences with non-uniform current distributions that are still cylindrically symmetric, indicating a broader consideration of cases in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether to use current density ##J## or total current ##I## for larger diameter wires, indicating multiple competing views remain on the topic.

Contextual Notes

Participants acknowledge the potential for varying current distributions and the implications of wire geometry on the calculations, but do not resolve the specific conditions under which each approach should be applied.

PhiowPhi
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Most of the problems I've worked on involve wires of small radii, however, if DC current flows within large radii of conductive wires, would I need to use current density ##J## for calculating the magnetic field at a point ## r > R## instead of ##I## if it we're known?

With relevance to a wires with large radii, would ampere's law change? Or still valid regardless of large or small radii? Also, in relation to that matter, does the Lorentz force alter with the change of geometry of the wire(e.g large radius, shorter lengths etc...)?
 
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I'm not sure as to when current density ##J## might be used in calculating the magnetic field and Lorentz force acting on a wire placed in a magnetic field. If a clarification of that could be posted would greatly help.
 
PhiowPhi said:
Most of the problems I've worked on involve wires of small radii, however, if DC current flows within large radii of conductive wires, would I need to use current density JJ for calculating the magnetic field at a point r>R r > R instead of II if it we're known?
(I'm assuming R is the radius of the wire)

If the current density J is distributed with cylindrical symmetry around the axis of the wire, then you can use the total current I to calculate the magnetic field outside the wire. That is, you can pretend that the total current is "collapsed" into a line along the central axis of the wire.

This is analogous to the situation where you want to find the electric field outside a charge distribution: if the charge density ρ has spherical symmetry, you can pretend that the total charge is "collapsed" into a point at the center.
 
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Well, if the wire is carrying DC isn't it intuitive to assume current is uniformly distributed? Therefore, using ##I## would suffice for these types of problems?
 
I've done and assigned exercises in which the current distribution is not uniform, but is still cylindrically symmetric. I just wanted to touch all the bases, because around here, if I don't, someone will probably come along and do it for me. :oldeyes:
 

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