physica Posted October 22, 2014 Share Posted October 22, 2014 I have been reading about how dipoles produce an inverse cube law. The sad thing is that I can't find any maths behind it. Am I reading a crackpot theory? If not could someone post the maths or give a link to the maths? Link to comment Share on other sites More sharing options...
Carrock Posted October 22, 2014 Share Posted October 22, 2014 I have been reading about how dipoles produce an inverse cube law. The sad thing is that I can't find any maths behind it. Am I reading a crackpot theory? If not could someone post the maths or give a link to the maths? There is quite a lot of useful information here: https://www.physicsforums.com/threads/magnetic-force-inverse-cubed-law.587204/ Link to comment Share on other sites More sharing options...
swansont Posted October 22, 2014 Share Posted October 22, 2014 Write down the field of two monopoles of opposite charge, separated by an infinitesimal amount. Expand the denominator Link to comment Share on other sites More sharing options...
Enthalpy Posted October 22, 2014 Share Posted October 22, 2014 The cube is correct for a dipole, I confirm. Remember this is for a static field or slowly varying. If the charges, currents... vary significantly within one propagation time between the poles, then you obtain a part as a propagating field which decreases less quickly. Link to comment Share on other sites More sharing options...
physica Posted October 29, 2014 Author Share Posted October 29, 2014 Thanks guys this has helped a lot. Link to comment Share on other sites More sharing options...
physica Posted November 6, 2014 Author Share Posted November 6, 2014 Coming back to this topic, why would Gauss's law still be valid if Coulomb's was replaced by an inverse cube law? Link to comment Share on other sites More sharing options...
Enthalpy Posted November 6, 2014 Share Posted November 6, 2014 It's still valid for each charge of the dipole. Only the net effect, as the difference between two forces in 1/R2, changes as 1/R3. Link to comment Share on other sites More sharing options...
swansont Posted November 6, 2014 Share Posted November 6, 2014 Coming back to this topic, why would Gauss's law still be valid if Coulomb's was replaced by an inverse cube law? It wouldn't be. Consider a spherically symmetric scenario — the law works because the flux drops off as r^2 and so does the surface area of a sphere. That's not the case for an inverse-cube relation. IOW, E.dA is not a constant — it varies with r. 1 Link to comment Share on other sites More sharing options...
Enthalpy Posted November 7, 2014 Share Posted November 7, 2014 If the dipole consists of two finite charges with finite separation, each feels a force as 1/R2 from a distant one. In that sense, Coulomb's law still applies. Link to comment Share on other sites More sharing options...
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