The magnetic field of a loop at its centre be B.
And the radius of the loop be R.
And the no of turns be n.
Now B is directly proportional to n
And B is inversely proportional to R.
Hence B1=B=k/rhence k=Br
Where k is proportionality constant.
n=1 R=r
Now the wire has n turns hence if the radius is r1 then total length is 2pi *r1*n and it's equal to 2pi*r
Hence r1=r/n
Then B2=kn/r1=Br *n/(r/n)=Bn^2.