In: Physics
An ideal solenoid holds a current ?. Use Ampere’s Law to show that the magnetic field strength inside the solenoid is ?=?0??.

n = number of turns per unit length
L = length considered
I = total current
consider a ampere's closed loop PQRS
B.
dl = 
B. dl Cos0 = B L
B.
dl = 
B. dl Cos90 = 0
B.
dl = 
(0). dl   = 0
B.
dl = 
B. dl Cos90 = 0
So
B.dl
= 
B. dl + 
B. dl + 
B. dl + 
B. dl
B.dl
= BL + 0 + 0 + 0
B.dl
= BL
according to ampere's law
B.dl
= 
NI
So
BL = 
NI
B = 
(N/L)I
B = 
(n)I