# Why skin effect happens at the center of a conductor?

I was reading an article about Skin Effect. I know what skin effect is, but I wanted to know what causes it.

Why is the back EMF strongest at the center? Why is it not distributed uniformly at the cross section area of the conductor? so that, the main current is resisted but passes through both the centre and surface.

Here is the article I was reading: https://en.wikipedia.org/wiki/Skin_effect

• It probably takes some calculus to prove it, but I think the most magnetic field lines (from all the imaginary infinitesimally thin conductors that make the cable) overlap their fields maximally at the center of the conductor. A bit of googling found a simulation: fermi.la.asu.edu/w9cf/skin/skin.html (as well as a math proof after it).
– Fizz
Nov 12, 2015 at 15:10
• Since you are probably looking for the physics behind this, I don't know if maybe on physics.SE you might get a better answers. Anyways for all the field lines (IW in the image) draw them equidistant, and then look at the whole thing from above... Nov 12, 2015 at 15:11
• An copper conductor having radius 10mm,10km length. Given Tax at 20°C=(1.77×15 raise to the power -8)ohm_m.Temperature constant=241°C,find change in R due to skin effect Jun 23, 2020 at 2:02
• The conducting electrons are not forced to the outside of the conductor. That's simply wrong. (After all, the charge-density is not being altered.) Instead, the carriers nearer the surface are experience a significant net force directed parallel to the wire. Electrons near the center are not. Jun 23, 2020 at 2:25

The magnetic intensity, H integrated along a loop is equal to the current enclosed. So for a longer loop (the blue lines in your figure), a given current will produce a smaller intensity. The maximum intensity (which creates the maximum EMF) occurs with the smallest loop (i.e. in the center).

A solid conductor may thought to be consisting of large no. of strands, each carrying small part of the current. The inductance will vary according to its position. Thus the strands near the centre are surrounded by a greater magnetic flux and hence larger inductance than that near the surface. The high reactance of inner strands cause the alternating current to flow near the surface of the conductor.

Let me try to explain this with following 2 assumptions-

1. Suppose current is flowing through hollow concentric cylinders instead of a solid cylindrical conductor.
2. Initially current started flowing uniformly through all the concentric cylinders.

So the hollow cylinder with least radius will have strongest magnetic field (least sized cross-section circle) and vice versa, because the amount of current passing through each hollow cylinder should be same.

Putting all the calculus aside, the image is self explanatory. If you look at the direction the currents are moving towards, eddy currents induced by changing magnetic field(and therefore, the back EMF) are interfering constructively outside the magnetic loops (going to same direction) and interfering destructively inside the magnetic loops (going to inverse direction). Think of the infinite amount of those magnetic loops concentrated around each other on each cross-section on the wire,(as noted on Priya's answer) and it becomes clearer that more inverse current applies in the core of the conductor.

• Hi, welcome to the site. This question was answered long ago. Please concentrate in newer and/or unanswered questions Jan 27, 2017 at 9:41
• Thank you for the answer, it's really helpful. I always prefer putting maths aside and understand the physical phenomenon. Jan 27, 2017 at 13:19