For a continuous eigen-basis the basis vectors are not normalizable to unity length. They can be normalized only upto a delta function. At the same time for discrete eigen basis the basis vectors are normalizable to unity length.
What about the systems with both discrete as well as continuous...
Atran,
The question you have formulated is not simple as it looks. And that is because there are lot of complexities associated with the situation.
The distribution of the charge (since they are free to move on a conductor) itself is dependent on the shape, relative orientation of the...
Yes, This is a valid point. But that brings another question. If the conductor is of some arbitrary shaped closed loop (neither a circle nor any closed figure with any particular symmetry, it can be non-planar also). Is it correct to say that the argument still holds? Please give reasons also??
The electrons moving in the Ring are not moving in a straight line (on an average). In other words they are accelerating. Any accelerating charge should radiate em field. This is a standard result in classical electrodynamics. So invariably these electrons also should radiate em energy...
The superconductor itself is in the form of a ring and if we throw a magnet through the center of this ring current should inevitably be formed in the ring right??
I am sorry for framing the question that way. But the point in the question was not that at all. If there is a dc current in a...
by theoretically not possible I do not mean about the finite small resistance (however small it might be) and instead the radiation effects of the accelerating electrons in the Coil (since it is not a straight conductor)
Suppose that, a sudden current pulse has been generated (by means of a Magnet) in a Super-Conducting Loop (or coil). It is commonly said that the current remain there forever. Is is true?? I mean will the current remain in the loop undiminished till t=infinity? But theoretically it isn't...
In the Lab Frame the -ve charge carriers are moving whereas the +ve charge carriers are at rest (Supposing that the current is due to flow of electrons). So the -ve charge carriers can be treated as a second frame which will experience Lorentz Contraction because of which the wire should appear...
Thanks for the reply.
But I think I have not put the question very clearly. Actually there are no different situations discussed in the question. There is only one situation. i.e., There is a TEST CHARGE at a fixed point away from a Steady Current Carrying Infinite Wire. Since the TEST...
Consider an infinitely long stationary conductor which carries a steady uniform current.
1. At an arbitrary Test Point outside the conductor the Electric Field should be ZERO according to Maxwell's Equation.
2. But if Special theory of Relativity is considered, the moving charges...