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 = 5.55·10-4 m and is made of copper having a density of ? = 8960 kg/m3. The gun consists of rails of length L = 1.42 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 1.11·104 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

F=ILB
a=ILB/M=ILB/(*volume)=

=1.03·104 A*1.48 m *2.07 T/(8960 kg/m3*pi*(5.63·10-4 m)^2)

=2.39*10^6 m/s^2
v=(2*a*L)=2605.3 m/s

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