The magnetic field inside a tightly wound,long solenoid is B = u (not) ni.It suggests that the field does not depend on the total length of the solenoid,and hence if we add more loops at the end of the solenoid,the field should not increase.Explain qualitatively why the extra-added loops do not have a considerable effect on the field inside the solenoid.

Question

dls · Answer

@Mashy @yrelhan4

anonymous · Answer

that is pretty shimple..

anonymous · Answer

If the windings are tightly coiled.. effectively the field at any point is only due to the loops that are very close to it..

dls · Answer

whyyyyyyy?

theeric · Answer

That equation gives the near uniform magnitude of the magnetic field in the space that's surrounded by the coil. But you assume that the solenoid is VERY long, so that the coils on the end don't have much of an effect on the magnetic field in the middle where you look at.

anonymous · Answer

what why!?

check your expression for the B field due to a circular coil far away from the centre.. the field becomes very very small.. so you can totally neglect the field due to the coils far away..hence adding more loops effectively doesn't change the field.. but if you TIGHTEN the loops on the other hand.. then u increase the B field.. cause if you make it more tightly coiled.. then number of loops near any point will be higher..

theeric · Answer

In short, I guess, $B=\mu_0\ n\ I$ is an estimate, that is inaccurate with coils that have small lengths compared to radii. The number of coils does not matter, then, because it's an estimate and you assume an infinite length (very large length compared to radius).

That assumption was one piece of the puzzle to deriving $B=\mu_0\ n\ I$, I believe. If you wanted to be more exact, you would derive an equation specific to your solenoid. However, I don't think the magnetic field would be as uniform with the short coils of large radii.

I put a lot of dense information in there. Any questions on it?

anonymous · Answer

@Mashy how is B field dependent on the ditance of the point from the centre? the equation is B= u (not)ni. it does not include the distance!