Rail guns and gauss (or coil) guns are different - rail guns require significantly higher electrical current than a coil gun.
Quoting from Wikipedia: " Coilguns are distinct from railguns, as the direction of acceleration in a railgun is at right angles to the central axis of the current loop formed by the conducting rails. In addition, railguns usually require the use of sliding contacts to pass a large current through the projectile, but coilguns do not necessarily require sliding contacts."
Similar end though - no black powder of combustible accelerant.
The future will be multi-stage coil guns.
Bizarrely, I too built a similar electric field accelerated projectile device in my A-level physics class, in 1986! I too did it ‘economically,’ using items I found around the house and in the physics lab. Admittedly, we were building HF power amplifiers at home which did help.
I missed the boat by about 80 years - first designs were early 1900s.