Given,
Volume of iron rod is, V=10−3m3
Relative permeability, μr=1000
No of turns per unit length of solenoid is, n=lN=10turnscm−1=1000turnsm−1
Current through the solenoid is, i=0.5A
Magnetic moment of an iron core solenoid is given by,
M=(μr−1)NiA
⇒M=(μr−1)NilV=(μr−1)lNiV
⇒M=(1000−1)×1000×0.5×10−3
⇒M=499.5≈500Am2