= Magnetic coenergy
{title2=$W'_B=\sum_i I_i\lambda_i-W_B$}
For reversible quasistatic magnetic circuits with <flux linkages> $\lambda_i$, currents $I_i$ and mechanical coordinate $q$, write $dW_B=\sum_i I_i\,d\lambda_i-F_q\,dq$. The <Legendre transform> $W'_B=\sum_iI_i\lambda_i-W_B$ obeys $dW'_B=\sum_i\lambda_i\,dI_i+F_q\,dq$. Thus $F_q=(\partial W'_B/\partial q)_{I_i}$, while $F_q=-(\partial W_B/\partial q)_{\lambda_i}$. In a linear reciprocal system $W'_B=W_B=\tfrac12\mathbf I^{\mathsf T}L(q)\mathbf I$ numerically, but the variables held fixed in their <force> <derivatives> differ. The coenergy formulation includes the effect of electrical sources maintaining the currents; it avoids reversing the sign of the magnetic <force> by differentiating stored <energy> under the wrong <constraint>.
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