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aim1732
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If a time varying magnetic field of infinite dimensions crosses a plane at right angles what can we expect induced electric field lines to look like? Straight lines with direction determined by the right hand rule?
hikaru1221 said:I'm not sure how the B-field looks like, but you may want to consider the picture
Abdul Quadeer said:But we have to accept the question at its face value without arguing against it
hikaru1221 said:I'm not saying it doesn't exist in just real life. I'm saying it doesn't exist, even in theory
It's just like asking how your house would look like if you ran at v = 10c.
hikaru1221 said:I'm saying it doesn't exist, even in theory
Abdul Quadeer said:Prove
stevenb said:Some hypothetical thought experiments (infinite plane waves, infinitely long wires, uniform charge density over all space etc.) are at least compatible with Maxwell's equations even if they are not physically realizable.
hikaru1221 said:@stevenb: If I use a plane wire carrying varying current, the B-field at every point in the plane of the wire should be perpendicular to the plane, regardless of retardation, I guess. If so, I still have an infinite varying B-field which crosses a plane at right angle and matches the criteria of the OP
hikaru1221 said:My assertion is based on the assumption that the OP was talking about an infinite B-field with a lack of a center. The B-field must come from some source, either a current setup or varying E-field. But even if it's varying E-field, the E-field must in turn come from some real source, which is charge setup (Abdul Quadeer, you may want to look back to my post in one of your thread ). The setup cannot be infinitely large, so a center should be determined (see my picture in my previous post). If the setup is infinitely large, the energy needed to drive this source is infinite.
@Abdul Quadeer: They are compatible if there is no violation Think of my example of v=10c, an obvious violation
Abdul Quadeer said:We have situations like this- an infinitely long current carrying wire. Where does the source of driving this infinite charge come from? Is it not a violation?
The OP's latest question was regarding the logic in fixing a centre. I rechecked your picture and found that you too arbitrarily fixed a centre in the plane.
hikaru1221 said:Similarly, if you look at the space locally, it would look like to you that the setup is infinite and the field is just the same at every other points in the space, but they are actually not.
hikaru1221 said:The emphasis of the picture is on the current source. This is where the center comes from. The imaginary plane has nothing to do with the center of the field. The shape of the field depends on the source, and thus, since the source is finite, that constraints the field in a sense that there is a center.
Abdul Quadeer said:How can you ascertain that the field is not same everywhere? It may or may not be depending upon the source.
How will you define a magnetic field of infinite dimensions (given in the question) from a finite source?
hikaru1221 said:By the way, you may want to prove that uniform infinite B-field doesn't exist in the constraint of finite source, say, a current source. Hint: Apply Ampere Law at the current.
hikaru1221 said:B-field is inherently infinite (in the extent of classical physics). It's just that it must have a determined center - that's the point.
Abdul Quadeer said:The field is time-varying, not uniform.
'Apply Ampere Law' to what?
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 .
aim1732 said:The setup hikaru showed is just one of the possibilities----- I had an infinite wire carrying current in mind whose current varies with time.
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].
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?
No one forbids you to solve a free fall problem with Lagrangian.
aim1732 said:Sadly I do not know that much calculus as yet.
An induced electric field is a type of electric field that is generated when a magnetic field changes or crosses a conducting material, such as a metal plane. This change in magnetic field induces a flow of electrons, creating an electric field.
Induced electric field lines are represented as closed loops that are perpendicular to the direction of the changing magnetic field. These lines form circles around the direction of the magnetic field and show the direction of the induced electric field.
The induced electric field is always perpendicular to the magnetic field. This means that the direction of the induced electric field is always at a 90-degree angle to the direction of the changing magnetic field.
The strength of the induced electric field is directly proportional to the strength of the changing magnetic field. This means that as the magnetic field becomes stronger, the induced electric field also becomes stronger.
Induced electric fields have many practical applications, including in generators, transformers, and electric motors. They are also used in technologies such as wireless charging and electromagnetic induction cooktops.