In the iron-based superconductors, both nematic and magnetic fluctuations are expected to enhance superconductivity and may originate from a quantum critical point hidden beneath the superconducting dome. The behavior of the non-superconducting state can be an important piece of the puzzle, motivating in this paper the use of high magnetic fields to suppress superconductivity and measure the nematic susceptibility of the normal state at low temperatures. We describe experimental advances which make it possible to measure a resistive gauge factor (which is a proxy for the nematic susceptibility) in the field-induced normal state in a 65 T pulsed magnet, and report measurements of the gauge factor of a micromachined single crystal of Ba(Fe$_{0.926}$Co$_{0.074}$)$_2$As$_2$ at temperatures down to 1.2 K. The nematic susceptibility increases monotonically in the field-induced normal state as the temperature decreases, consistent with the presence of a quantum critical point nearby in composition.
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