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[itex]\cdot[/itex]dl=[itex]\mu[/itex]I n=N/L Biot-Savart: B=[itex]\mu[/itex]IN/(2[itex]\pi[/itex]r 3. The attempt at a solution Solving Ampere's Law gives you BL=[itex]\mu[/itex]IN and so N=BL/([itex]\mu[/itex]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/([itex]\mu[/itex]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!