Question

i'm confused with equation solenoid B= u.NI/L vs muti-loop B=u.NI/2PIR vs single-loop B=u.I/2R

u. is mu(not)= 4piE^-7

i don't know when to use each once of them.

since only different is diving by L or 2piR or sometimes 2R really confused.

Answer 1

in first B= u.NI/L

first u need to know what is N/L for N/L is number of loop per unit length

often they call in small n and the field beclame

B= u.n*I   

if you have multi-loop like N loop then u need to find out the length of wire  

suppose u have N loop on radius of R coil

then the length of wire = L = N*2*pi*r

N/L = 1/ ( 2*pi*r) = n  

so total field became = N* u.n*I = N*u* 1/ ( 2*pi*r) * I

and last  

B=u.I/2R this is the field due to coil on center it is not related to solenoid problem

if u want more explanation let me know i will be happy to help