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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 a X = + 36H? ƏH T 1-т/т. and we, (r), f(H) T. (1 – T/T.)? 1 1 Мо 1 ƏT 2 T. (1 — Т/T.)4/2 ? 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. %3D (a) State what is meant by a function of state. (b) Find f(H). (b) Find M(H,Tт). (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 a X = + 36H? ƏH T 1-т/т. and we, (r), f(H) T. (1 – T/T.)? 1 1 Мо 1 ƏT 2 T. (1 — Т/T.)4/2 ? 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. %3D (a) State what is meant by a function of state. (b) Find f(H). (b) Find M(H,Tт). (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.

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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 a X = + 36H? ƏH T 1-т/т. and we, (r), f(H) T. (1 – T/T.)? 1 1 Мо 1 ƏT 2 T. (1 — Т/T.)4/2 ? 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. %3D (a) State what is meant by a function of state. (b) Find f(H). (b) Find M(H,Tт). (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.
Transcribed Image Text: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 a X = + 36H? ƏH T 1-т/т. and we, (r), f(H) T. (1 – T/T.)? 1 1 Мо 1 ƏT 2 T. (1 — Т/T.)4/2 ? 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. %3D (a) State what is meant by a function of state. (b) Find f(H). (b) Find M(H,Tт). (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.
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