1The formula you gave is valid for a solenoid of infinite length.
An infinite solenoid, on addition of a few turns, remains an infinite solenoid.
1no actually the q ispractically adding more loops mean the intensity of magnetic field mst increase na (however the change cud be small ) bt theorotically its constant .why?
1n=no. of turns per unit length
1
metal
·2009-05-01 09:14:17
Arey, B=μ0ni is a completely theoretical concept------- hypothetical------ Don't mix it with practical things-------- you don't get infinite solenoids in practice.
If you consider a very long solenoid------ the magnetic field at abround the centre of the solenoid can be approximated by B=μ0ni
If you add loops, the field will increase but that will be a negligible increase------- so that the magnetic field at the centre can still be approximated by B=μ0ni
Please wait till tomorrow. I'll post the expression for the field inside a
"practical" (having finite length) solenoid. You'll see that as it's
length->∞ , B->μ0ni
1
metal
·2009-05-01 20:01:22
Here's the derivation for expression for the field in the middle of a solenoid of length L, number of turns n, current flowing "i" , and Radius R.
Field at centre due to an element dx (ring) at a distance x = dB =( μ0niR2dx)/2(R2+x2)3/2
So, net field = B = -L/2∫L/2 ( μ0niR2dx)/2(R2+x2)3/2
i,e. B= μ0niL /√(4R2+L2)
As you can see, with increase in L, B increases but the increase is negligible for large L.
And for L>>R , B≈ μ0ni
[I posted this, even though you've already understood, because I said I would do so.]