# Induced E field

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.

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Good to see some interest.

The setup hikaru showed is just one of the possibilities----- I had an infinite wire carrying current in mind whose current varies with time. At distances very far away from the wire we can draw planes containing the current source such that the field crosses perpendicularly,is nearly straight(a result of large distance from source) and is very nearly constant. But it would still have an axis of symmetry by virtue of being produced by a current source---that is the wire itself.How do you suggest the vortex field lines to then look like? If the wire were finite we would have taken the centre of the wire as the centre of the vortex but the wire is infinite and it's field is quite different from that of a finite source.[If the center of vortex were to lie on the wire it would make the induced E field lines very nearly straight too as I said in my first post].

I know you would say an infinite wire can still have a centre--like it is divided into two rays infinite on either side. I am not going to argue about that anymore because I realise well that something not existing in nature can not be expected to be governed by physical laws.
An interesting related situation(rather simple): The E field of an infinite charged plane is independent of distance. It is useful when calculating stuff for it but ever tried to calculate a potential for it? It is strange but I think that in order to predict hypothetical situations sometimes we need to drop some of the more basic ideas,as in,what kind of conservative electrostatic field requires infinite work to b performed on a charge to just bring it in the frame?

The setup hikaru showed is just one of the possibilities----- I had an infinite wire carrying current in mind whose current varies with time.

The setup can never be truly infinite, if it's a closed circuit First, you need to close the circuit. Second, the energy to drive the circuit cannot be infinite.
I can give you an example of a truly infinite current: you use some mechanism that "shoots" electrons to free space. The electrons expand in some directions in the space and may form infinite currents (currents that are not confined within limited space). However, the true source of this current is the mechanism, and this mechanism, again, cannot be infinite.

How do you suggest the vortex field lines to then look like? If the wire were finite we would have taken the centre of the wire as the centre of the vortex but the wire is infinite and it's field is quite different from that of a finite source.[If the center of vortex were to lie on the wire it would make the induced E field lines very nearly straight too as I said in my first post].

E-field lines are approximately straight at the points near the wire. If you think of a closed circuit at a larger extent, the vortex will be somewhere within the loop. The vortex is of the E-field as a whole and thus can be at anywhere in the space, so we cannot look at the picture locally at points near the wire - we have to look at the whole picture.

something not existing in nature can not be expected to be governed by physical laws.

As stevenb said, even if it is not realizable in reality, it is still valid as long as there is no violation with the law of nature. However, an infinite setup is not that case.

An interesting related situation(rather simple): The E field of an infinite charged plane is independent of distance. It is useful when calculating stuff for it but ever tried to calculate a potential for it? It is strange but I think that in order to predict hypothetical situations sometimes we need to drop some of the more basic ideas,as in,what kind of conservative electrostatic field requires infinite work to b performed on a charge to just bring it in the frame?

I think that's because a uniform E-field says much more than a field with V=Cx (C=const) No one forbids you to solve a free fall problem with Lagrangian.

No one forbids you to solve a free fall problem with Lagrangian.

Sadly I do not know that much calculus as yet.

Sadly I do not know that much calculus as yet.

Basically I mean, some people find it easier to work directly with E-field in that case, instead of its potential But convenience is subjective 