An insulating rod of length l carries a charge q distributed uniformly on it.The rod is pivoted at an end and is rotated at a frequency f about a fixed perpendicular axis.The magnetic moment of the system is?

let the charge density on rod be λ = q/l

consider a small element of rod dx at a distance x from the fixed end

 charge on it dq = λ dx

when the rod rotates  the current due to this element , di = f dq

                                                                                 = f λ dx

magnetic moment of this current  element dM = di * area

                                                                = f λ dx * ∏ x^2

total magnetic moment M = ∫ dM =

                                               = ∫₀ ^l  f λ dx * ∏ x^2

                                                = fλ∏ ∫₀ ^l ₍ x^2 ) dx  

                                                 =  fλ∏/3 * x^3 ]^{₀ l}

                                                 =  fλ∏ l^3 /3         

λ l = q , so

         M =  f∏q l^2  /3