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EM fields. Angular Momentum seems not to be Conserved!
Hi everyone..
This is a paradox which as been stated in Feynman Lectures 2 (Chapter 17-4).
What Feynman is telling is, there is a plastic plate which is free to rotate about an axis passing through the center of the disc, there are several metal spheres having a charge Q which are sticked to the plate. Now at the centre of the plate there is a current carrying solenoid of some length put in a way that the axis of the solenoid coincides with the axis of the disc. The solenoid is made of a supercondcuting material. And the temp is right now let's say 0.1 K.
Now as the temp increases the superconductivity is lost and hence the current is lost. So the flux of B decreases(for an Amperian loop concentric to the solenoid) and hence that creates an E which will try to reduce the decrease in the flux. Now this E inturn applies a force to the charged metal spheres.
Hence there is a net force on the plate. Hence the disc rotates. The disc has some angular momnetum. But intially the angular momentum is zero. So what's happening? Is the law of conservation of momentum wrong?
My thoughts-
Law of conservation is a beautiful truth of nature. It cannot be wrong.
There are two outcomes.
1)The plate doesnot rotate. Then momentum is conserved. But then why does the disc doensot rotate?
2)The plate does rotate. In this case what i have come to think is that. If i change the charge of the spheres to -Q from +Q. The final angular momentum will have a changed direction. And now as my initial momentum should be equal to final. My inital momentum s thus depndent on the charge of the metal spheres. And this is absurd. How can the Initial momentum depend on the charge of the spheres unless there is something like the momentum of the fields which interacts with the spheres and stuff like that...
So help me with it. Dont give the answer. Give me a hint or an argument which might help me get out of this wonderful paradox.
Hi everyone..
This is a paradox which as been stated in Feynman Lectures 2 (Chapter 17-4).
What Feynman is telling is, there is a plastic plate which is free to rotate about an axis passing through the center of the disc, there are several metal spheres having a charge Q which are sticked to the plate. Now at the centre of the plate there is a current carrying solenoid of some length put in a way that the axis of the solenoid coincides with the axis of the disc. The solenoid is made of a supercondcuting material. And the temp is right now let's say 0.1 K.
Now as the temp increases the superconductivity is lost and hence the current is lost. So the flux of B decreases(for an Amperian loop concentric to the solenoid) and hence that creates an E which will try to reduce the decrease in the flux. Now this E inturn applies a force to the charged metal spheres.
Hence there is a net force on the plate. Hence the disc rotates. The disc has some angular momnetum. But intially the angular momentum is zero. So what's happening? Is the law of conservation of momentum wrong?
My thoughts-
Law of conservation is a beautiful truth of nature. It cannot be wrong.
There are two outcomes.
1)The plate doesnot rotate. Then momentum is conserved. But then why does the disc doensot rotate?
2)The plate does rotate. In this case what i have come to think is that. If i change the charge of the spheres to -Q from +Q. The final angular momentum will have a changed direction. And now as my initial momentum should be equal to final. My inital momentum s thus depndent on the charge of the metal spheres. And this is absurd. How can the Initial momentum depend on the charge of the spheres unless there is something like the momentum of the fields which interacts with the spheres and stuff like that...
So help me with it. Dont give the answer. Give me a hint or an argument which might help me get out of this wonderful paradox.