Question

Two infinitely long slits, S1 and S2, each of width d=0.1 cm are used to prepare a box-shaped electron beam with energy E=400 eV. At what distance x from the slit S2 will the thickness of this electron beam double due to Coulomb's repulsion? The linear density of electron current (as measured right after the slit S2) is i=.0001 A/cm. (Hint: linear density of current i is the total electron current I divided by the length of the slit L. Consider the electron beam as an infinitely large plane of charge, in such conditions surface charge density can be found as i/v, where v is the electron's velocity after the slit S2).