- #1
vsv86
- 25
- 13
Hello Everyone
This question is motivated by a small calculation I am doing on polarization of bodies in external electric field.
What I wanted to do is this:
1) Mesh the region
2) Prescribe uniform (and non-changing) positive charge distribution
3) Prescribe (initially) uniform negative charge density (net charge is zero)
4) Vary the negative charge density, i.e. shuffle the charges between mesh elements
5) Calculate the potential (##\phi##) due to distributed charge density (##\rho##)
6) Compute energy ##U=\int{d^3 r (\phi+\phi_{ext})\rho}##, where ##\phi_{ext}## is due to applied field
7) If the energy has decreased, keep the new negative charge distribution, otherwise go back to the previous distribution
8) Repeat from step 4 onwards., keep going until it converges
What I realized now is that minimization of energy is justified from thermodynamic considerations, i.e. this is a restatement of the second law. This means however, that I now need to understand what is the relationship between the energy of charges in the electromagnetic field, which I would usually extract from the Hamiltonian, and the energy of the system in the thermodynamic sense. I expect the two must be the same, but I am finding it hard to justify it with non-handwave'y arguments.
Can anyone suggest a some literature (or a simple argument) on the matter?
Kind regards
PS: All of this is for electrostatics
This question is motivated by a small calculation I am doing on polarization of bodies in external electric field.
What I wanted to do is this:
1) Mesh the region
2) Prescribe uniform (and non-changing) positive charge distribution
3) Prescribe (initially) uniform negative charge density (net charge is zero)
4) Vary the negative charge density, i.e. shuffle the charges between mesh elements
5) Calculate the potential (##\phi##) due to distributed charge density (##\rho##)
6) Compute energy ##U=\int{d^3 r (\phi+\phi_{ext})\rho}##, where ##\phi_{ext}## is due to applied field
7) If the energy has decreased, keep the new negative charge distribution, otherwise go back to the previous distribution
8) Repeat from step 4 onwards., keep going until it converges
What I realized now is that minimization of energy is justified from thermodynamic considerations, i.e. this is a restatement of the second law. This means however, that I now need to understand what is the relationship between the energy of charges in the electromagnetic field, which I would usually extract from the Hamiltonian, and the energy of the system in the thermodynamic sense. I expect the two must be the same, but I am finding it hard to justify it with non-handwave'y arguments.
Can anyone suggest a some literature (or a simple argument) on the matter?
Kind regards
PS: All of this is for electrostatics