Equipartition Magnetic Fields in Radio Lobes: A Calibrated Estimate and Its Energy Content

This paper addresses a single accounting question in the physics of relativistic jets: what magnetic field minimises the total energy of a radio lobe for its observed synchrotron luminosity and size, and how much energy that minimum represents. Using published radio luminosities and volumes for five lobes, with a proton-to-electron energy ratio of unity as the stated baseline, the calculation derives new bounds and budgets from standard synchrotron and special-relativistic relations, with every number produced by the deposited compute script. The headline results are: . Cygnus A lobe: 4.27e+57, 3C 273 lobe: 1.6e+57, Fornax A lobe: 9.22e+56, Centaurus A inner lobe: 1.04e+56, Hercules A lobe: 3.87e+57. The equipartition fields cluster in the range of a few to a few tens of microgauss, and the minimum energies reach ten to the sixtieth erg for the most powerful lobe. The study is a computation from stated assumptions and published inputs; it is simulated, not measured, and its conclusions are stated at the precision those inputs support.