  We derive the minimum power of jets and their magnetic field strength based
on their observed non-thermal synchrotron emission. The correct form of this
method takes into account both the internal energy in the jet and the ion
rest-mass energy associated with the bulk motion. The latter was neglected in a
number of papers, which instead adopted the well-known energy-content
minimization method. That method was developed for static sources, for which
there is no bulk-motion component of the energy. In the case of electron
power-law spectra with index >2 in ion-electron jets, the rest-mass component
dominates. The minimization method for the jet power taking it into account was
considered in some other work, but only based on either an assumption of a
constant total synchrotron flux or a fixed range of the Lorentz factors.
Instead, we base our method on an observed optically-thin synchrotron spectrum.
We find the minimum jet power is independent of its radius when the ion
rest-mass power dominates, which becomes the case below certain critical
radius. This allows for robust minimum power estimates. We also present results
for the case with observed turnover frequency, at which the source becomes
optically thick. This method allows a determination of the source size, in
addition to the power and the magnetic field. We also point out that when the
ion rest-mass power dominates, the estimates of the minimum power lead to very
different equipartition parameters than those based on minimization of the
energy content. The former and latter lead to approximate equipartition between
the internal energy in magnetic field and in particles including and excluding,
respectively, their rest mass energy.
