A device called a railgun uses the magnetic force on currents to launch projecti

Question

A device called a railgun uses the magnetic force on currents to launch projectiles at very high speeds. An idealized model of a railgun is illustrated in (Figure 1) . A 1.2 V power supply is connected to two conducting rails. A segment of copper wire, in a region of uniform magnetic field, slides freely on the rails. The wire has a 0.71 m resistance and a mass of 5.6 g . Ignore the resistance of the rails. The power supply is switched on.

What is the current?What is direction of the force on the wire?What is the magnitude of the force on the wire?

What will be the wire's speed after it has slid a distance of 6.0 cm ?

Explanation / Answer

we know that

V = IR. v =1.2 v and R = 0.71m ohm I = V/R = 1.2/0.71x10-³ = 1.69x10³ A

also ,

Force = I * L * B. You have the current I, the length L, the magnetic field B

F = IlxB = 1.69x10³(0.15)(0.8) = 202.8 N

F = ma = 0.056a = 202.8,

a = F/m = 202.8/0.045 = 3621.42 m/s²

also, kinetic energy = (1/2)mv^2

v² = 2ax = 2*3621.42*0.06 = 2*4506.66*0.06 = 434.57

v = 434.57 = 20.84 m/s ans

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