Existing data up to momentum transfers of $Q2 \sim$ 1.5 (GeV/c)$^2$ are compatible with the Galster ``parameterization'', an empirical fit to data on $G_{E_n}$ obtained at lower values of $Q2$. Recent theoretical investigations, which were motivated by the results of Jlab experiments 93-027 and 99-007 on the ratio of the proton electric and magnetic form factor, predict higher values of $G_{E_n}$ compared to Galster at higher momentum transfers.
Experiment 02-013 at Thomas Jefferson National Accelerator Facility will extend the measured range of the neutron electric form factor $G_{E_n}$ to $Q2$=3.4 (GeV/c)$^2$ through a measurement of the cross section asymmetry in the reaction $^3\vec{He}(\vec{e},e'n)$.
The experiment utilizes the Hall A polarized $^3$He target and the polarized CEBAF beam at moderate beam energies. Scattered electrons will be detected in the BigBite spectrometer, recoiling neutrons in an array of scintillators. Because of the high kinetic energy of the neutrons, a high neutron detection efficiency and at the same time an excellent background suppression can be achieved.
After a brief review of our present knowledge on the electromagnetic form factors of the nucleon, I will focus on the experimental and theoretical developments which are essential to perform Jlab experiment E02-013. Concepts of extending the measurement of $G_{E_n}$ to even higher momentum transfers will be discussed briefly.