- #1

potatowhisperer

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**1.**

the problem goes like this :

The energy of interaction of a classical magnetic dipole with the magnetic field B is given by

E = −μ·B.

The sum over microstates becomes an integral over all directions of μ. The direction of μ

in three dimensions is given by the angles θ and φ of a spherical coordinate system

The integral is over the solid angle element

= sin θdθdφ. In this coordinate system

the energy of the dipole is given by E = −μB cos θ.

Choose spherical coordinates and show that the probability p(θ, φ)dθdφ that the dipole is

between the angles θ and + dθ and φ and φ + dφ is given by

p(θ, φ)dθdφ = (e^(

2. Homework Equations

the problem goes like this :

The energy of interaction of a classical magnetic dipole with the magnetic field B is given by

E = −μ·B.

The sum over microstates becomes an integral over all directions of μ. The direction of μ

in three dimensions is given by the angles θ and φ of a spherical coordinate system

The integral is over the solid angle element

= sin θdθdφ. In this coordinate system

the energy of the dipole is given by E = −μB cos θ.

Choose spherical coordinates and show that the probability p(θ, φ)dθdφ that the dipole is

between the angles θ and + dθ and φ and φ + dφ is given by

p(θ, φ)dθdφ = (e^(

**μB cos θ**) sin(**θ) d****θ d****φ)/z**2. Homework Equations

z = ∫∫

**e^(μB cos θ) sin(**

**θ) d****θ d****φ .**## The Attempt at a Solution

i have no idea what to do , and i tried all i know

i know that the Boltzmann distribution gives you the probability that a particle has an energy is :

e^([/B]μB cos θ)/∫

**e^(**μB cos θ) , but how do i integrate the spherical coordinates i don t know . please help me and thank you .

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