2) The magnetization of a ferromagnet can be described by a function of state M(T, H) where T and H are its temperature and external magnetic field respectively. For T < Te, the magnetic susceptibility x of this ferromagnet and its temperature coefficient can be modeled by the following equations (ƏM X = a + 36H? , 1-T/T. T. аnd (), 1 Мо f(H) T. (1 – T/T.)² 2 T. (1 – T/T.)'/2 ' where Mo = M(T = 0, H = 0) > 0, a > 0 and b > 0 are constants, T, is the critical temperature and f(H) is function of H with the property f(H = 0) = 0. ƏM 1 1 ƏT (a) State what is meant by a function of state. (b) Find f(H). (b) Find M(H,T). (d) Sketch the plot M(H,T) as a function of T for the cases where H = 0. What happens to the magnetization at T = T? (e) Consider the case where H > 0. In the limit when T_ → Te, where the minus subscript indicates we approach the limit from T < Te, calculate the critical exponent for x.

2) The magnetization of a ferromagnet can be described by a function of state M(T, H) where T and H are its temperature and external magnetic field respectively. For T < Te, the magnetic susceptibility x of this ferromagnet and its temperature coefficient can be modeled by the following equations (ƏM X = a + 36H? , 1-T/T. T. аnd (), 1 Мо f(H) T. (1 – T/T.)² 2 T. (1 – T/T.)'/2 ' where Mo = M(T = 0, H = 0) > 0, a > 0 and b > 0 are constants, T, is the critical temperature and f(H) is function of H with the property f(H = 0) = 0. ƏM 1 1 ƏT (a) State what is meant by a function of state. (b) Find f(H). (b) Find M(H,T). (d) Sketch the plot M(H,T) as a function of T for the cases where H = 0. What happens to the magnetization at T = T? (e) Consider the case where H > 0. In the limit when T_ → Te, where the minus subscript indicates we approach the limit from T < Te, calculate the critical exponent for x.