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We report on new NuSTAR and archival Chandra observations of the pulsar windnebula (PWN) 3C 58. Using the X-ray data, we measure energy-dependentmorphologies and spatially-resolved spectra of the PWN. We find that the PWNsize becomes smaller with increasing energy and that the spectrum is softer inouter regions. In the spatially integrated spectrum of the PWN, we find a hintof a spectral break at $\sim$25 keV. We interpret these findings usingsynchrotron-radiation scenarios. We attribute the size change to thesynchrotron burn-off effect. The radial profile of the spectral index has abreak at $R\sim80''$, implying a maximum electron energy of $\sim$200 TeV whichis larger than a previous estimate, and the 25-keV spectral break correspondsto a maximum electron energy of $\sim$140 TeV for an assumed magnetic fieldstrength of 80 $\mu$G. Combining the X-ray data and a previous radio-to-IR SED,we measure a cooling break frequency to be $\sim 10^{15}$ Hz, which constrainsthe magnetic-field strength in 3C 58 to be 30-200$\mu$G for an assumed agerange of 800-5000 years.

{\it NuSTAR} hard X-ray studies of the pulsar wind nebula 3C~58