Can i derive magnetic field inside a solenoid using magnetic field due to a circular coil carrying current on its axis?

Question

anonymous · Answer

Sure... if you know the expression for the magnetic field from a single coil then what do you suppose the magnetic field will be if you have N coils?

anonymous · Answer

uNI/2r
Is it correct?

anonymous · Answer

Yup :)

anonymous · Answer

But this is definitely not equal to what we get when we use Ampere's Circuital Law...
We get unI there...

anonymous · Answer

Do you have a diagram of the situation?  We might be on different pages.

anonymous · Answer

Two long coaxial insulated solenoids, S1 and S2 of equal lengths (L) are wound one over the
other as shown in the figure. A steady current "I" flow through the inner solenoid S1 to the
other end B, which is connected to the outer solenoid S2 through which the same current "I"
flows in the opposite direction so as to come out at end A. If n1 and n2 are the number of turns
per unit length, find the magnitude and direction of the net magnetic field at a point (i) inside
on the axis. 
Now, to solve it, Can I use  $$\mu nLI/2r$$

anonymous · Answer

attachment

anonymous · Answer

Hmm I'm working it out now....

anonymous · Answer

So according to Ampere's law, yeah you'd end up with
$$B =\mu _{0}NI$$ ... which is the right answer for a solenoid.

It turns out that what I suggested to you initially doesn't describe a solenoid, but rather something called a toroid.  That is my fault, I apologize :(

anonymous · Answer

where N this time is the number of turns per unit length.  That is... the loop density.

anonymous · Answer

Thanks...:)