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The neutron electromagnetic form factors, G_Eⁿ and G_Mⁿ, give important insights into the neutron structure. Previous experiments measured the proton electromagnetic form factors G_E^p up to Q² = 8 GeV²  and G_M^p up to Q² = 10.2 GeV², while G_Eⁿ has only been measured up to Q² = 3.5 GeV². The proton electric form factor data showed unexpected features at high Q² values, where no G_Eⁿ data is available. The SBS program at JLab plans to measure G_Eⁿ/G_Mⁿ at Q² values of 1.5, 3.8, 6.8, and 10.2 GeV² by colliding a polarized electron beam with a polarized ³He target, used here as an effective polarized neutron target,  and measuring the transverse asymmetry of the cross section. G_Eⁿ values can be extracted using high Q² G_Mⁿ data from a companion experiment. Scattered electrons will be measured in the BigBite spectrometer upgraded with the addition of a Gas Electron Multiplier (GEM) based tracker. Scattered neutrons are magnetically separated from scattered protons and will be detected in an array of scintillators. At our highest Q² point we expect to be able to calculate the form factor ratio with an accuracy better than Δ(G_Eⁿ/G_Mⁿ) = 0.20, which corresponds to ΔG_Eⁿ = 3 x 10^-4 with accurate measurements of G_Mⁿ.