Magnetic Field of a Finite Solenoid

[bmbuncher]

Homework Statement
Find the magnetic field generated at the center of a coil of wire with N turns, a radius of r, and a current I running through it
Relevant equations
B=μ₀nI, where n=N/L (L is the total length of the coil)
The attempt at a solution
B=μ₀nI
B=μ₀I(N/L)
L=2πrN
B=(μ₀NI)/(2πrN)
B=(μ₀I)/(2πr)

However, the correct answer is:
B=(μ₀I)/(2r)

Why is this? Thank you!

 

[Bashkir]

The equation you have given I believe only applies to a "long" solenoid. This is a good approximation as you can see, but it isn't enough. Consider how we would find the magnetic field at the center of ring? Now consider how we would find the find at the center of a collection of rings. Is the answer the same? Should it be the same?