first read this carefully
 
consider a charge moving in a circular path ...let radius of its path of radius r ...
due to its motion it a current is produced along the path ...then motion this particle 
can be compared to a charged ring of radius r, circulating with some angular velocity...
 
magnetic moment = M = IA = I(pir2)               .........................1


 
we have to calculate magnetic moment for rod , let mid point of rod is O ...
now  consider two small elements dq of thickness dx on the rod which are at distance x from center
on both sides...
this (dq+dq) charge is moving in circle so producing current ...
total charge= 2dq
charge per unit length = q/L
dq = (q/L)dx  so
total charge = (2q/L)dx                     .........................2
total  current over 1 complete revolution (t = 2pi/w) = total charge/t =  (wq/piL)dx    .......3            (w = angular frequency)
area of circle  = pix2 so
magnetic moment = (total current)(area)
                          =pix2(wq/piL)dx
                    dM = (wq/L)x2dx
integrating both sides
          M = (wq/L) (x3/3)             lim 0 to L/2
          M = (wq/L)(L2/24)
          M = wqL2/24   
now , w = 2pif so
        M = piqL2/12
this is the required result