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How are bound charges in a dielectric "in equilibrium"?

Physics Asked by Chris Yang on July 28, 2021

In Griffiths E&M, he provides two equations with regard to the energy of a system. The first being
begin{equation}label{eq:1}
W = frac{epsilon_0}{2}intlimits_{text{all space}} E^2 mathrm{d}tau tag{1}
end{equation}

In a linear dielectric system he claims that the energy is instead
$$ W = frac{epsilon}{2}intlimits_{text{all space}} E^2 mathrm{d}tau $$
or, written more succinctly
begin{equation}label{eq:2}
W = frac{1}{2}intlimits_{text{all space}} mathbf{D}cdotmathbf{E} mathrm{d}tau tag{2}
end{equation}

He claims that the discrepancy between ref{eq:1} and ref{eq:2} comes from the fact that they reference different energies. ref{eq:1} gives the energy needed to take all the free and bound charges from infinity to their spots, which he claims gives $W = W_{text{free}}+W_{text{bound}}$. This, however, does not take into account the work involved in stretching and twisting the dielectric molecules. ref{eq:2} on the other hand gives the energy required just to bring all the free charge into place (the bound charges spring into existence with their addition), and Griffiths claims that ref{eq:2} does take into account the work of stretching and rotating, since the force required to bring the free charges in is dependent on the disposition of the bound charges. So for ref{eq:2},
$$W_{text{total}} = W_{text{free}}+W_{text{bound}}+W_{text{spring}}$$
He finally claims that $W_{text{bound}}$ and $W_{text{spring}}$ are equal and opposite by virtue that the bound charges are always "in equilibrium" and hence the net work done on them is zero, and hence $W_{text{total}} = W_{text{free}}$. In what sense are bound charges in equilibrium, and how does this make the net work done on them (to move some free charges in from infinity) zero?

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