# Editing Curie's law

**Warning:** You are not logged in. Your IP address will be publicly visible if you make any edits. If you **log in** or **create an account**, your edits will be attributed to your username, along with other benefits.

The edit can be undone.
Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.

Latest revision | Your text | ||

Line 44: | Line 44: | ||

This is magnetization of one paramagneton, total magnetization of the solid is given by | This is magnetization of one paramagneton, total magnetization of the solid is given by | ||

− | : | + | |

+ | <blockquote style="border: 1px solid black; padding:10px;"> | ||

+ | <math>M = N\left\langle\mu\right\rangle = N \mu \tanh\left({\mu B\over k T}\right)</math></blockquote> | ||

The formula above is known as the [[Langevin]] [[Paramagnetic]] equation. | The formula above is known as the [[Langevin]] [[Paramagnetic]] equation. | ||

Pierre Curie found an approximation to this law that applies to the reasonably high temperatures and low magnetic fields used in his experiments. Let's see what happens to the magnetization as we specialize it to large <math>T</math> and small <math>B</math>. As temperature increases and magnetic field decreases, the argument of hyperbolic tangent decreases. Another way to say this is | Pierre Curie found an approximation to this law that applies to the reasonably high temperatures and low magnetic fields used in his experiments. Let's see what happens to the magnetization as we specialize it to large <math>T</math> and small <math>B</math>. As temperature increases and magnetic field decreases, the argument of hyperbolic tangent decreases. Another way to say this is | ||

− | :<math>\left({\mu B\over | + | :<math>\left({\mu B\over k T}\right) << 1</math> |

this is sometimes called the '''Curie regime'''. We also know that if <math>|x|<<1</math>, then | this is sometimes called the '''Curie regime'''. We also know that if <math>|x|<<1</math>, then | ||

:<math>\tanh x \approx x</math> | :<math>\tanh x \approx x</math> | ||

− | + | so | |

− | : | + | <blockquote style="border: 1px solid black; padding:10px;"> |

+ | :<math>\mathbf{M}(T\rightarrow\infty)={N\mu^2\over k}{\mathbf{B}\over T}</math></blockquote> | ||

+ | |||

+ | Q.E.D. | ||

== More Involved Derivation (Statistical Mechanics) == | == More Involved Derivation (Statistical Mechanics) == |