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 = 4.3 10-4 m and is made of copper having a density of ? = 8960 kg/m3. The gun consists of rails of length L = 1.0 m in a constant magnetic field of magnitude B = 1.8 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 1.10 104 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.) 1

Explanation / Answer

Magnetic force is given as:

F=ILB

density=M/Volume

M=density*Volume

Volume=*(4.3*10-4)^2*1

a=ILB/M

=ILB/(density*volume)=
=1.1*104*1*1.8/(8960*pi*(4.3*10-4)^2)
=3.8*10^6 m/s2

Resistance of copper = *L/A

=1.72*10^-8

L = 1 m

A=*(4.3*10-4)^2

Resistance = 0.0296

Time taken to flight :

t= B*A/R*I

=1.8**(4.3*10-4)^2/( 0.0296*1.1*104)

=3.5312*10^-9

Thus final velocity:

V =u+a*t

=0+3.8*10^6*3.5312*10^-9

=0.01342 m/s

OR

13.42 cm/s

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