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  (miliohms) resistance and a mass of 4.8 g . Ignore the resistance of the rails. The power supply is switched on.

Part A

What is the current flwoing through the copper wire?

Part B

What is direction of the force on the wire?

Part C

What is the magnitude of the force on the wire?

Part D

If the amount of friction is negligible, what will be the wire's speed after it has slid a distance of 8.0 cm ?

Explanation / Answer

a)

the current flwoing through the copper wire

I=V/R =1.2/(0.71*10-3)=1690.14 A

b)

right

c)

the magnitude of the force on the wire

F=BIL =0.8*1690.14*0.15=202.8 N

d)

acceleration of rod

a=F/m =202.8/0.0048 =42254 m/s2

the wire's speed after it has slid a distance of 8 cm is

V=sqrt[2ad]=sqrt[2*42254 *0.08]

V=82.22 m/s

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