We report results from a study on electrical breakdown in liquid helium using near-uniform-field stainless steel electrodes with a stressed area of $sim$0.725 cm$^2$. The distribution of the breakdown field is obtained for temperatures between 1.7 K and 4.0 K, pressures between the saturated vapor pressure and 626 Torr, and with electrodes of different surface polishes. A data-based approach for determining the electrode-surface-area scaling of the breakdown field is presented. The dependence of the breakdown probability on the field strength as extracted from the breakdown field distribution data is used to show that breakdown is a surface phenomenon closely correlated with Fowler-Nordheim field emission from asperities on the cathode. We show that the results from this analysis provides an explanation for the supposed electrode gap-size effect and also allows for a determination of the breakdown-field distribution for arbitrary shaped electrodes. Most importantly, the analysis method presented in this work can be extended to other noble liquids to explore the dependencies for electrical breakdown in those media.
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