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Just curious about the history of electric flux

-Flux-

I am aware of the fact that flux, on its own is a mathematical concept but how did it find its way into physics. Was it just introduced to replace the E.A in gauss law or maybe in an attempt to explain inverse square law. Or was it because physicists were experimenting by using all possible operations on vector fields?

-Field lines-

I have a similar doubt regarding regarding field lines. I believe that they were probably introduced to explain the inverse square law by saying that the lines of force get distributed over a surface of a sphere and thus vary inversely with the square of distance. Am i correct? Thx for any help

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  • $\begingroup$ These concepts were inspired by flux and stream lines (of a velocity field) in hydrodynamics, see e.g. Lamb (1895, pp. 20, 41, etc.). $\endgroup$ – Francois Ziegler Oct 14 '18 at 22:40
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The line of force, in physics, is the path followed by an electric charge free to move in an electric field or generally any appropriate test particle in a given force field.

More abstractly, lines of force are lines in any such force field the tangent of which at any point gives the field direction at that point

and the density of these field lines gives the magnitude of the field.

To investigate the nature of electric force between charges -** Coulomb had performed an experiment using Torsion balance and the inverse square law could be verified for electric field between charges .**

The concept of lines of force was introduced into physics in the 1830s by the English scientist Michael Faraday, who considered magnetic and electric effects in the region around a magnet or electric charge as a property of the region rather than an effect taking place at a distance from a cause.

The electric lines of force that represent the field of a positive electric charge in space consist of a family of straight lines radiating uniformly in all directions from the charge where they originate.

A second positive charge placed in the field would travel radially away from the first charge.

By relating the strength of the Electric field to the density of lines of force crossing unit area of a surface perpendicular to the flux lines led to inverse square dependence on radial distance.

The concept of Maxwell's tubes of forces were also defined and as area crossing through the field lines or tubes varies as the inverse square of the distance(thereby the density of lines of force will decrease as inverse square) it was understood that the nature of field strength will vary as 1/ r^2.

Ref.- https://www.britannica.com/science/line-of-force

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  • $\begingroup$ 1) The link seems paywalled. 2) Is this cut and pasted? Blockquote (yellow) should indicate this, what then do italics / bold mean? 3) This is full of mistakes large and small. “Later” Coulomb (1736-1806)? The path of a “mass free to move in a gravitational field” is not a line of force (in constant gravity the former is a parabola, the latter a vertical line). This holds in the velocity fields of hydrodynamics, from which Maxwell (1855, pp. 30 sq) took the concepts of flux and flow lines (Bernoulli’s “efflux”, Euler, D’Alembert). $\endgroup$ – Francois Ziegler Oct 14 '18 at 21:53
  • $\begingroup$ @Francois Ziegler- the answer has been corrected. and Encyclopedia Brittanica is a free site..not paywalled. $\endgroup$ – drvrm Oct 15 '18 at 13:38
  • $\begingroup$ An “electric charge free to move in an electric field” does not follow a line of force of the field: again consider a constant field $\mathbf E$. Also, not everything is from the linked page, is it? $\endgroup$ – Francois Ziegler Oct 15 '18 at 13:58
  • $\begingroup$ @FrancoisZiegler- the yellow marked statements are from the linked page.If one keeps a charge Q at say point P-then a unit +charge will move in the direction of the field and the path traced is the lines of force. At any point, on the path, the tangent will give the direction of the force. If however another charge is in the environ the lines of force will be curved, either repulsive or attractive- the density of the lines -crossing a unit area defines the strength of the field- this flow of lines is the flux- this is elementary electrostatics-check from any inter level physics book. $\endgroup$ – drvrm Oct 15 '18 at 17:36
  • $\begingroup$ @FrancoisZiegler- thanks for your comments- you are raising the issue of constant value of Electric field, but only in magnitude, as around a charge distribution equipottential surfaces can be built ,whose negative rate of change may be constant, which defines the magnitude of field but at each point on the surface the field direction will be outward and perpendicular to elementary surface area ds-those are flux of field lines of forces- as you go to larger distances, the area will increase as square of distance and line density will decrease as 1/r^2. The density of flux lines defines E. $\endgroup$ – drvrm Oct 15 '18 at 17:46

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