- #1
faheemahmed6000
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Hi everyone here. I have my question in the following attached pdf file
Confusion in Maxwell's derivation of Ampere's Force Law
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Discussion Overview
The discussion revolves around confusion regarding Maxwell's derivation of Ampere's Force Law as presented in his work "A Treatise on Electricity and Magnetism." Participants are examining specific equations and their implications within the context of Maxwell's theoretical framework, focusing on the transition from special cases to general cases in the derivation.
Discussion Character
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant expresses confusion about the validity of the equation ##P=\dfrac{B+C}{2r}## in the general case, questioning how it can be applied when the conditions change (0 < l, m, n < 1).
- The same participant seeks clarification on Maxwell's statement regarding eliminating P to find the general value of ##\dfrac{dX}{ds}##, suggesting that if ##P\neq\dfrac{B+C}{2r}##, the reasoning may be flawed.
- Another participant requests a detailed derivation of how equation 21 is obtained from equation 15, indicating a need for further mathematical exploration.
- There are indications that some participants are unsure if others will engage with the initial question due to its presentation in a PDF format.
Areas of Agreement / Disagreement
The discussion appears unresolved, with participants expressing confusion and seeking clarification on specific mathematical derivations and the application of Maxwell's equations. There is no consensus on the interpretations of the equations or the implications of Maxwell's statements.
Contextual Notes
Participants have noted the limitations of the initial question's presentation and the need for mathematical symbols, which may affect the clarity of the discussion. The reliance on specific conditions and the implications of changing parameters in Maxwell's equations are also highlighted as areas of uncertainty.
- #2
faheemahmed6000
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Sorry I didn't posted my question directly. It was because of unavailability of Maths symbols
- #3
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I doubt anyone else will read your file.
This site supports ##\LaTeX## ...
enclose your expression (say) \xi\nu with opening double-# and closing double-# to produce ##\xi\nu##
This site supports ##\LaTeX## ...
enclose your expression (say) \xi\nu with opening double-# and closing double-# to produce ##\xi\nu##
- #4
jtbell
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See here for an introduction: https://www.physicsforums.com/help/latexhelp/robphy said:
- #5
faheemahmed6000
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I am reading Maxwell's "a treatise on electricity and magnetism, Volume 2, page 156" about "Ampere's Force Law". I have some confusion in the following pages:
My question is of two parts:
1. Equation 20, i.e. ##P=\dfrac{B+C}{2r}## is the outcome of special case (i.e. l=1, m=0, n=0)
But in Page 156, Article 517, Maxwell says: "We can now eliminate P, and find the general value of ##\dfrac{dX}{ds}## and uses this formula (i.e. ##P=\dfrac{B+C}{2r}##) in the general case.
However in the general case, where 0 < l, m, n < 1, and hence
##\dfrac{d^{2}X}{dsds'}=l\left( \frac{dP}{ds'}\xi^{2}-\dfrac{dQ}{ds'}+(B+C)\dfrac{l'\xi}{r}\right) +m(...)+n(...)\neq0##
(since direction of X is not in the direction of ds)
therefore,
##\dfrac{dX}{ds}=l\left[ (P\xi^{2}-Q)_{(s',0)}-\int\limits_0^s' (2Pr-B-C)\dfrac{l'\xi}{r}ds'\right] +m\int\limits_0^s'(...)ds'+n\int\limits_0^s'(...)ds'##
Now in this general case, how can we get ##P=\dfrac{B+C}{2r}##.
If ##P\neq\dfrac{B+C}{2r}## in general case, what does Maxwell mean by "We can now eliminate P, and find the general value of ##\dfrac{dX}{ds}##"
2. How can one get equation 21 from equation 15. Please give a lengthy derivation.
My question is of two parts:
1. Equation 20, i.e. ##P=\dfrac{B+C}{2r}## is the outcome of special case (i.e. l=1, m=0, n=0)
But in Page 156, Article 517, Maxwell says: "We can now eliminate P, and find the general value of ##\dfrac{dX}{ds}## and uses this formula (i.e. ##P=\dfrac{B+C}{2r}##) in the general case.
However in the general case, where 0 < l, m, n < 1, and hence
##\dfrac{d^{2}X}{dsds'}=l\left( \frac{dP}{ds'}\xi^{2}-\dfrac{dQ}{ds'}+(B+C)\dfrac{l'\xi}{r}\right) +m(...)+n(...)\neq0##
(since direction of X is not in the direction of ds)
therefore,
##\dfrac{dX}{ds}=l\left[ (P\xi^{2}-Q)_{(s',0)}-\int\limits_0^s' (2Pr-B-C)\dfrac{l'\xi}{r}ds'\right] +m\int\limits_0^s'(...)ds'+n\int\limits_0^s'(...)ds'##
Now in this general case, how can we get ##P=\dfrac{B+C}{2r}##.
If ##P\neq\dfrac{B+C}{2r}## in general case, what does Maxwell mean by "We can now eliminate P, and find the general value of ##\dfrac{dX}{ds}##"
2. How can one get equation 21 from equation 15. Please give a lengthy derivation.
- #6
faheemahmed6000
- 16
- 0
Please somebody answer my question.
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