Plot the figure in part A and find X = dM/dH etc. in part B

-C.) where Bo - poft is the magnetic The Langevin function describing the field-dependent magnetization of superparamagnetic nanopalticles can be written, M(B.,7)=M, coth MB k 7 induction of a vacuum (a) Consider superparamagnetic maghemite (Fe3O4) nanoparticles, for which there is a moment of 1.4 Ha per Fe atom, and Ms is 4.8 x 10 A/m. Plot M(Bo, 300 K) for B, between +5 T for maghemite nanoparticles containing 100, 5,000, and 100,000 Fe atoms. dM dM (b) The magnetic susceptibility for these non-linear magnetization curves is x - 4 dB, Usually, X is measured at Bo-0. (In this problem, the analytical form of x has a discontinuity at Bom 0.) Find x at or near Bo - 0 for each of the three nanoparticle sizes in (a). Numerical (rather than analytical) solutions are acceptable and easier to perform. Note that y is a unitless quantity, and the units should entirely cancel out. dH