A rail gun accelerates a projectile from rest by using the magnetic force on a c

Question

A rail gun accelerates a projectile from rest by using the magnetic force on a current-carrying wire. The wire has radius r = 6.09·10-4 m and is made of copper having a density of ? = 8960 kg/m3. The gun consists of rails of length L = 1.18 m in a constant magnetic field of magnitude B = 2.01 T, oriented perpendicular to the plane defined by the rails. The wire forms an electrical connection across the rails at one end of the rails. When triggered, a current of 1.03·104 A flows through the wire, which accelerates the wire along the rails. Calculate the final speed of the wire as it leaves the rails. (Neglect friction.)

Explanation / Answer

magnetic force acting on the wire is F = BIL where B = 2.01 T,I = 1.03 * 10^4 A and L = 1.18 m centripetal force acting on the wire is F1 = mv^2/r where m = density * volume = p * pir^2L = 8960 * (22/7) * (6.09 * 10^-4)^2 * 1.18,v is speed of wire and r is radius Here,F = F1 or mv^2/r = BIL or v = (BIL * r/m)^1/2

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