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 0.78 m? resistance and a mass of 4.4 g . Ignore the resistance of the rails. The power supply is switched on.

What is the current?

What is the magnitude of the force on the wire?

Explanation / Answer

Here,

mass , m = 4.4 gm = 0.0044 Kg

R = 0.78 mOhm = 7.8 *10^-4 Ohm

for the current in wire

current in wire = V/R

current in wire = 1.2/(7.8 *10^-4)

current in wire = 1538.5 A

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magnitude of the force on the wire = B * I* L

magnitude of the force on the wire = 0.80 * 1538.5 * 0.15 N

magnitude of the force on the wire = 184.6 N

the magnitude of the force on the wire is 184.6 N

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let the speed after sliding 5 cm is u m/s

Using work energy theorum

0.5 * m * u^2 = F * d

0.5 * 0.0044* u^2 = 184.6 * 0.05

solving for u

u = 64.8 m/s

the speed of rod after sliding for 5 cm is 64.8 m/s

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