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I've learned in school that the force in a coil is $F=kx$, linear on how much the coil is stretched. Two questions:

  1. Is it always linear for every shape of a coil? Does it remain linear if we increase the radius of the coil, increase the length between loops and so on?

  2. Can we deduce the value of $k$ based on the geometry of the coil?

The motivation is that I know how to deduce the inductance of a coil based on its shape, but I haven't seen that calculation done to deduce the $k$ in Hooke's Law.

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There is part of the discussion here. Try to get the paper by alternative sources. I know the book Moyses Nussenzveig had a short treatment, but it isn't in English, afaik.You may search for the computation of elastic constants in Continuum mechanics. –  JuanPi Jun 8 '12 at 16:39
Related: physics.stackexchange.com/q/22894/2451 –  Qmechanic Jun 8 '12 at 17:19
Ah I answered that one :-) No upvote though :-( Ricbit, if question 22894 doesn't help maybe edit your question to indicate what's missing and I'll try to answer it here. –  John Rennie Jun 8 '12 at 18:10
Thanks for the answers, the wiki for Continuum Mechanics and the Springipedia solved my curiosity! springipedia.com/compression-shape-sizes.asp –  Ricbit Jun 10 '12 at 19:01

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