Magnetic and Electric Field Curiousity

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Now I preface this by saying that I am still very far from having any true appreciable amount of knowledge on the subject of electromagnetism, only about 2 semesters worth. I have been trying to actively learn a lot on my lonesome and this is something I felt worth asking.

I did not want to post this question elsewhere since it has nothing to do with school, just a personal muse.

Analyzing both Coloumb's Law and the Biot-Savart Law for electric and magnetic fields, I notice that the constants involved both contain 4pi and are inversely related to the distance squared.

Putting this factor together, 4pi*r^2, would be the surface of a sphere centered at the point we are measuring from.

Since 4pi*r^2 is in the denominator, this means either the electric field or magnetic field at a point is inversely proportional to it.

Now do these factors truly stem from inverse proportionality to the surface of a sphere centered about the point of interest, or do they come from other sources?

If so, would it be feasible to have a gravitational analog in the Law of Gravitation since it is also inversely related to distance squared? Perhaps we could simply factor out a G from 4pi. I know the last bit on gravitation is a stretch, but it seems like a cool idea.

Someone shed some light on this darkness!
 

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  • #2
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It's not clear what you're asking, but you might be interested to read up on the gravitomagnetic field (being verified by gravity probe B).
 
  • #3
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The 4pi factor is just a constant that appears when using SI (sisteme international) units. It depends on how the others constants (G, epsilonzero, muzero) where defined. The appearance of 4pi is NOT a law of nature.
 
  • #4
ZapperZ
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lpfr is correct. Try looking at the SAME two equations in CGS units. No more 4pi to trouble you.

Zz.
 
  • #5
Meir Achuz
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The 4\pi is from the total solid angle of a sphere, which is about what you have deduced. In Gauss's law for a point charge, the 4 pi is natural.
In trying to remove the 4 pi from G's law, SI "rationalizes", leading to distress for EM students.
The 2 pi is from the total angle of a circle. It is naural in Ampere's law for a long straight wire. SI rationizes that too, introducing the "fundamental" constant 12.6 X 10^-7, which has nothing to do with permeability.
 
  • #6
rbj
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Putting this factor together, 4pi*r^2, would be the surface of a sphere centered at the point we are measuring from.

Since 4pi*r^2 is in the denominator, this means either the electric field or magnetic field at a point is inversely proportional to it.

Now do these factors truly stem from inverse proportionality to the surface of a sphere centered about the point of interest, or do they come from other sources?

If so, would it be feasible to have a gravitational analog in the Law of Gravitation since it is also inversely related to distance squared? Perhaps we could simply factor out a G from 4pi. I know the last bit on gravitation is a stretch, but it seems like a cool idea.

Someone shed some light on this darkness!
i think you've done a commendable and insightful job of seeing a connection of concepts that they don't always teach so well in these first courses. Meir mentioned Gauss's Law, and i would add to that the concepts of flux and flux density. i would suggest looking up, in Wikipedia the articles on Flux, Inverse-square law, as well as Gauss's Law. come back with questions or clarifications after looking at that.
 
  • #7
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Thanks for all of the responses guys...you've given me insightful leads to search over.

Definitely will post something again once I do more research.
 

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