We report a measurement of the $ u_{mu}$-nucleus inclusive charged current cross section (=$sigma^{cc}$) on iron using data from exposed to the J-PARC neutrino beam. The detector consists of 14 modules in total, which are spread over a range of off-axis angles from 0$^circ$ to 1.1$^circ$. The variation in the neutrino energy spectrum as a function of the off-axis angle, combined with event topology information, is used to calculate this cross section as a function of neutrino energy. The cross section is measured to be $sigma^{cc}(1.1text{ GeV}) = 1.10 pm 0.15$ $(10^{-38}text{cm}^2/text{nucleon})$, $sigma^{cc}(2.0text{ GeV}) = 2.07 pm 0.27$ $(10^{-38}text{cm}^2/text{nucleon})$, and $sigma^{cc}(3.3text{ GeV}) = 2.29 pm 0.45$ $(10^{-38}text{cm}^2/text{nucleon})$, at energies of 1.1, 2.0, and 3.3 GeV, respectively. These results are consistent with the cross section calculated by the neutrino interaction generators currently used by T2K. More importantly, the method described here opens up a new way to determine the energy dependence of neutrino-nucleus cross sections.
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