# Magnetic and Electric Field Curiousity

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!

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).

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.

ZapperZ
Staff Emeritus
lpfr is correct. Try looking at the SAME two equations in CGS units. No more 4pi to trouble you.

Zz.

Meir Achuz
Homework Helper
Gold Member
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.

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.

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.