doubt3

The formula you gave is valid for a solenoid of infinite length.
An infinite solenoid, on addition of a few turns, remains an infinite solenoid.

n=no. of turns per unit length

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

kkkk thanks

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.]