Not very high velocities with this arrangement. Better would be successive coils with a timer that fires each one in turn further accelerating the projectile. Projectile of necessity must be ferrous and probably can't use rifling. Also, the coil, being and inductor, itself, cannot really generate a real sharp edge wave form as the nature of an inductor (coil) is to resist sudden current changes.
A more powerful solution is a rail gun. Still uses an inductor but the inductor is only 2 straight rails. They have a very low resistance to sudden surges of electricity. The bullet is any metal, not just ferrous.
The navy has demonstrated a rail gun launching a 7lb projectile at 5,400 MILES/Hour. That's about 51,000gr bullet at 7,920fps with a power factor of 408,000. We're talking MACH 7+ at sea level.
Problem is they haven't made these too small yet. Still "shipboard" size. And the current necessary for one shot, could light a major city. Think 100,000 to a million Amperes. Also the heat generated tends to shorten the life of the rails.
Oh, invented in 1917 by a French inventor and patented in 1920 in the US. Also known as a linear motor.