A rail gun accelerates a projectile from rest by using the magnetic force on a current-carrying wire.The wire has radius r = 5.10 × 10 − 4 m and is made of copper having a density of ρ = 8960 k g / m 3 . The gun consists of rails of length L = 1.00 m in a constant magnetic field of magnitude B = 2.00 T,oriented perpendicular to the plane defined by the rails. The wire forms an electrical connectionacross the rails at one end of the rails. When triggered, a current of 1.00 × 10 4 A flows through thewire, which accelerates the wire along the rails. Calculate the final speed of the wire as it leaves the rails.

Question

A rail gun accelerates a projectile from rest by using the magnetic force on a current-carrying wire.The wire has radius   r  =  5.10  ×      10          −      4           m and is made of copper having a density of   ρ  =  8960     k  g      /        m    3  . The gun consists of rails of length L = 1.00 m in a constant magnetic field of magnitude B = 2.00 T,oriented perpendicular to the plane defined by the rails. The wire forms an electrical connectionacross the rails at one end of the rails. When triggered, a current of   1.00  ×      10    4       A flows through thewire, which accelerates the wire along the rails. Calculate the final speed of the wire as it leaves the rails.

Alexandria Rubio · Accepted Answer

The above problem belongs to the topic of magnetism. It involves the concept of magnetic force due to a current carrying wire. We know that,Mass of wire   =  ρ  V  =  ρ  ×  (      4    3    )  π      r    3  where,   ρ = density of wire and V = Volume of wireMass,   M  =  ρ  V  =  8960     k  g      /        m    3    ×  (      4    3    )  ×  π  ×  (  5.10  ×      10          −      4           m      )    3    M  =  4.98  ×      10          −      6           k  gTherefore, Magnetic Force acting on the wire, F = Bil      M    a    =  B  i  lwhere, a = acceleration, B = strength of magnetic field, i = current flowing in wire, and l =  lengtha = Bil / M  a  =            [      2      ×      1.00      ×              10        4            ×      1      ]        4.98    ×      10          −      6        a  =  0.4  ×      10          10           m      /        s    2  Required velocity v is given by      v    2    =  2  a  l    v  =  [  2  a  l      ]                  1        2                v  =  [  2  ×  0.4  ×      10          10        ×  1      ]                  1        2                v  =  8.94  ×      10    4       m      /    s

The wire forms an electrical connection across the rails at one end of the rails. When triggered, a current of 1.00 xx 10^4 A flows through the wire, which accelerates the wire along the rails. Calculate the final speed of the wire as it leaves the rails.

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