5. Real world applications: An interesting application of electro-magnetic induc

Question

5. Real world applications: An interesting application of electro-magnetic induction is to build a rail gun. The fundamental design is illustrated in the diagram below. There is a potential difference between the two rails that allows a current to flow when a metal bar is placed on the rails, completing the circuit. There is an external magnetic field (created by magnets) in between the rails. The interaction between that external field and the current in the metal bar accelerates the bar along the rails.

Conduct a feasibility study: Design a rail gun to launch a metal bar at 300m/s, similar to the speed of a bullet. There are a number of parameters you need to constrain: 1) the current in the circuit, b) the strength of the magnetic field, c) the distance between the rails, d) the mass of the metal bar, and e) the length of the rails (and consequently the overall size of the gun). Note that these parameters are interrelated, so always keep in mind how changing one will affect your choice for another. I'll give you a few hints: a) It is hard to constrain the circuit current. The higher the current the more likely you are to melt the rails and weld the bar to the rails. Let's just assume that 100 Amps is the most you can put through the circuit. b) The strength of the field and the distance between the rails can be constrained by your choice of magnet.

DIAGRAM:
upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Railgun-1.svg/2000px-Railgun-1.svg.png

Explanation / Answer

Let the magnetic field used be B.

Let the current be i

length of rod is l

length of Rails be L

F=Bli

ma=Bli

a=Bli/m

v2=2as=2aL=2BlLi/m

given that i=100 A , v=300m/s

3002=2*BLl*100/m

150=BLl/m

We have to design it such that B*L*l/m =150m2/(A-s2)

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