Figure is an idealized schematic drawing of a rail gun. Projectile P sits between two wide rails of circular cross section; a source of current sends current through the rails and through the (conducting) projectile (a fuse is not used).

(a) Let w be the distance between the rails, R the radius of each rail, and i the current. Show that the force on the projectile is directed to the right along the rails and is given approximately by

(b) If the projectile starts from the left end of the rails at rest, find the speed y at which it is expelled at the right. Assume that i = 450 kA, w = 12 mm, R = 6.7 cm, L = 4.0 m, and the projectile mass is 10g

w + R In F = -1.- Source