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Question
A 10 g bullet with a charge of 4.00 μC is fired at a speed of 270 m s−1 in a horizontal direction. A vertical magnetic field of 500 µT exists in the space. Find the deflection of the bullet due to the magnetic field as it travels through 100 m. Make appropriate approximations.
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Solution
Given:
Mass of the bullet, m = 10g
Charge of the bullet, q = 4.00 μC
Speed of the bullet in horizontal direction, v = 270 m/s
Vertical magnetic field, B = 500 μT
Distance travelled by the bullet, d = 100 m
Magnetic force,
`vecF = q vecv xx vecB ....(i)`
Also,
F = ma
Using equation (i) we can write:
`ma = q vecv xx vecB`
`a = (qvB)/m `
Time taken by the bullet to travel 100 m horizontally,
`t = d/v = 100/270s`
Deflection due to the magnetic field in this time interval,
`y = 1/2at^2`
`= 1/2 xx (4.00 xx 10^-6 xx 270 xx 500 xx 10^-6)/(10xx10^-3) xx (100/270)^2`
= 3.7 × 10 -6 m.
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