Why skin effect happens at the center of a conductor?
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-
- Suppose current is flowing through hollow concentric cylinders instead of a solid cylindrical conductor.
- 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.