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.

Answer 1

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,
$\overrightarrow{F}=q\overrightarrow{v}\times \overrightarrow{B}$ ....(i)
Also,
F = ma
Using equation (i) we can write:
$ma=q\overrightarrow{v}\times \overrightarrow{B}$
$a=\frac{qvB}{m}$
Time taken by the bullet to travel 100 m horizontally,
$t=\frac{d}{v}=\frac{100}{270}\mathrm{s}$
Deflection due to the magnetic field in this time interval,
$$\begin{gathered} y=\frac{1}{2}a{t}^2 \\ =\frac{1}{2}\times \frac{4.00\times {10}^{-6}\times 270\times 500\times {10}^{-6}}{10\times {10}^{-3}}\times {\left(\frac{100}{270}\right)}^2 \\ =3.7\times {10}^{-6}\mathrm{m}. \end{gathered}$$