The field is time-varying, not uniform.
'Apply Ampere Law' to what?
"Time-varying" is the opposite of "constant"; "uniform" is the opposite of "non-uniform"
Anyway I just mean to show you that a uniform infinite B-field doesn't exist. Don't bother that problem until you get through this
I don't get you. In the first quote you say that infinite B-field doesnot exist for a finite source. In the second quote you say that it is infinite .
No, what I mean is that infinite B-field without a center doesn't exist And uniform B-field doesn't exist either. B-field can be uniform locally, but when we look at the whole picture, it is not uniform.
P.S.: I think the issue of uniformity, infinity and center thingy is the source of confusion. People usually visualize an infinite field as a field with straight field lines only, i.e. uniform field. If such field exists, it has no center (so "uniform" = "no center"). However, fields of Nature are usually infinite, whereas they are actually non-uniform. "Infinite" is not "uniform".
Another source of confusion is that people usually use the words "infinite" and "uniform" without being aware of the constraints. They are NOT using those words literally. "Infinite" only means very large / spreading over a large space, and "uniform" only means approximately the same in the considered space.