Elctromagnetic induction by a solenoid moving with the speed of light?

[A Dhingra]

Elctromagnetic induction by a solenoid moving with the speed of light??

The moment the magnetic field is generated, it should take some time to reach some distance. It cannot reach infinity instantly, it should have some speed, and that speed cannot be more than that of light. So let’s say that the newly generated magnetic field, through a current carrying wire, travels with the speed of light. Now for the application of the faraday’s law, let’s bring a magnet near a solenoid, through which initially no current flows, and make the magnet move with the speed of light. Will there be electromagnetic induction observed in this case?

Take another case, when instead of a magnet we have a different circuit containing a solenoid through which current flows when the switch is made on, and this circuit is held stationary moving the other one with the speed of light. Will there be electromagnetic induction observed in this case? What I think is that, as the system without current is moving as fast as the magnetic field … it never gets the chance to cut the magnetic field and cause induction to occur in the solenoid. So there should be no induction. But there is relative motion between the two systems and (also there is NO time varying magnetic field through the moving solenoid,)AND no induced current will be produced ...
so will the induction take place or not...??
if induction does not take place then the principle or relativity goes wrong...

 

[Dale]

make the magnet move with the speed of light

You cannot make a magnet move with the speed of light. It is a physically impossible premise, so you shouldn't be surprised that assuming it leads to contradictions.

 

[A Dhingra]

... can't it be just a thought experiment like many other paradoxes available...

with that assumption, think about the result...

 

[Dale]

No, think about the question:

make the magnet move with the speed of light. ... then the principle or relativity goes wrong...

Obviously, if you violate the principle of relativity in your question then the answer must be that the principle of relativity is violated. It is just the most basic logic. Non-physical assumptions lead to non-physical conclusions. This says nothing whatsoever about physics, only about your question.

 

[A Dhingra]

ok...
i agree that the situation is not realistic...
but still i didn't like the fact that one should not think beyond the laws made by humans himself...

 

[Dale]

This is elementary logic. If you have any set of axioms (A) which logically imply some result (B) then if your premise is not(B) then you must logically conclude not(A). This is called transposition and is one of the fundamental rules of logic: http://en.wikipedia.org/wiki/Transposition_(logic )

SR logically implies that a solenoid must move slower than light (STL), therefore if you assume that a solenoid can move with the speed of light you must logically conclude that special relativity (SR) is violated. Written in the usual format for logic:
(SR → STL) ↔ (~STL → ~SR)

Whether or not the situation is realistic and whether or not SR is a "law made by humans himself" is actually only a secondary concern. This is primarily an exercise in basic logic. Note that I am agreeing with your OP. Under the stated premise (~STL) you must indeed logically conclude that "the principle of relativity goes wrong" (~SR).

 

[vector22]

to make the experiment fair you would have to calculate what would happen to the solenoid at half light speed and then go from there.

 

[netheril96]

ok...
i agree that the situation is not realistic...
but still i didn't like the fact that one should not think beyond the laws made by humans himself...

If you want to think beyond relativity, invent your own laws of physics. If you want to explain in terms of relativity, then think within relativity.

 

[A Dhingra]

to make the experiment fair you would have to calculate what would happen to the solenoid at half light speed and then go from there.

can you help me go about finding this result...
(considering the magnetic field to be varying with time ... as it is getting produced .)