A railgun is a device that uses magnetic forces to launch projectiles at very hi

Question

A railgun is a device that uses magnetic forces to launch projectiles at very high speeds. An idealized model of a railgun is illustrated below. 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 resistance of 0.85 ohm (the resistance of the rails is negligible) and a mass of 5.0 g What is the current when the power supply is switched on? What is the magnitude and direction of the force on the copper wire? What will be the wire's speed after it has slide a distance of 6.0 cm?

Explanation / Answer

here,

V = 1.2 V

resistance , R = 0.85 ohm

mass , m = 0.005 kg

B = 0.8 T

a)

the current in wire , I = V/R

I = 1.2/0.85

I = 1.41 A

b)

the magnitude of the force on the copper wire , F = I * L X B

F = 1.41 * 0.15 * 0.8

F = 0.169 N

the force on the copper wire is 0.169 N towards right

c)

accelration of wire , a = F/m = 0.169/0.005

a = 33.88 m/s^2

d= 0.06 m

let the final speed be v

using third equation of motion

v^2 - u^2 = 2 * a * s

v^2 - 0 = 2 * 33.88 * 0.06

v = 2 m/s

the wire speed is 2 m/s

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