# Homework Help: Calculating Magnetic Fields in Solenoids vs. Current Loops and Coils

1. Mar 25, 2012

1. The problem statement, all variables and given/known data
There is a solenoid, with field B at its center, radius r, length L and maximum current I. Calculate the minimum number of turns the solenoid must have.

2. Relevant equations
Ampere's Law: (closed)∫B$\cdot$dl=$\mu$I
n=N/L
Biot-Savart: B=$\mu$IN/(2$\pi$r

3. The attempt at a solution
Solving Ampere's Law gives you BL=$\mu$IN and so N=BL/($\mu$I).

My question is why can't this same solution be found by solving with Biot-Savart, which is used for coils, according to my book? In that case, my answer is N=2Br/($\mu$I), and thus is off by a factor of 2r/L, or the diameter over the length of the solenoid.

Can someone please explain this to me? Thank you!

Last edited: Mar 25, 2012