Under intense electric field, the electrons emitted from the cathode by field emission have strong space charge effects, so the space charge limited current of a diode is an important parameter in the design of many intense electron beam apparatus, such as the high power microwave source devices. The field emission current density depends on cathode material and electric field at the cathode surface, while the space charge limited current density is a function of applied voltage and diode gap distance. To investigate the influence of the diode gap distance on space charge effect in field emission, in the paper we build a model of a planar vacuum diode operating with a field emission cathode. The time evolutions of the electric field at the cathode surface with various diode gap distance and applied voltage are studied using the particle-in-cell method, and the steady value of the electric field at the cathode surface is obtained. The electric field at the cathode surface first oscillates and finally reaches a steady state. At a given applied electric field, the longer the diode gap distance, the higher the absolute value of the electric field at the cathode surface is, and it takes more time to reach the steady state for longer diode gap distance; the distribution of the electric field in the diode gap region is steeper for shorter diode gap distance after the electric field at the cathode surface has reached a steady state.