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We know that when we connect a conductor to a source of potential difference, an electric field is established inside the conductor. With the help of calculations which I show below, we can see that electric field distribution inside the current-carrying conductor takes different forms depending on the shape of the conductor, independent of the resistivity and current density inside the conductor!

For example -

  1. Inside a straight cylindrical conductor, the electric field lines are uniformly distributed, independent of the resistivity of the conductor.

  2. Inside a circular conductor, the electric field lines vary as a function of "r".

I find out this distribution by using the property of the electric field that it's line integral in a closed-loop should be equal to zero.

My question is - Is there any "Intuitive" way we can predict the configuration of the electric field inside the current carrying conductor? How does the electric field inside the conductor decide, how to distribute? What parameters it considers and why it distributes the way it does? Why not in any other way?

The explanation, for example, points 1 and 2.

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  • $\begingroup$ When you eliminate the two "perpendicular" terms you already assumed $\vec{E}$ has only an axial component. Or else you assumed the integration path is symmetric about the center-line of the structure. $\endgroup$
    – The Photon
    Commented May 25, 2020 at 5:48
  • $\begingroup$ NO. From the formula, Electric Field = Resistivity * Current Density, we know that the direction of electric field at a point will be same as the current density, so I have used this knowledge to predict the directions of the electric field. With the help of calculations, I am only commenting on the magnitude. $\endgroup$
    – Devansh Mittal
    Commented May 25, 2020 at 7:01
  • $\begingroup$ My question is, is there something more fundamental available to know to predict the electric field lines configuration, apart from calculations? Do we have an intuitive method to reach the same conclusions I am reaching to, in the above calculations, with the help of mathematics? $\endgroup$
    – Devansh Mittal
    Commented May 25, 2020 at 7:03

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