Bullet Deflection in Magnetic Fields

How much is a bullet deflected by the Earth's Magnetic Field?

A 3.8g bullet is moving at 180m/s in the Earth's 5x10^-5T field. If the bullet has a charge of 8.1x10^-9C, by what distance will it be deflected after it has travelled 100m?

The magnitude of the force on the bullet at any time is given by the Lorentz force law:

F=qvB

a=F/m=qvB/m

At the first instant, the acceleration of the bullet is (neglecting gravity) a= 1.9x10^-8ms^-2

As this acceleration is very small it leads to a negligible change in velocity – so we’ll approximate the 100m as being in the original direction of travel and the force as being constant, due to a constant velocity of 180m/s.

The time taken to cross 100m is:

t=100/180s

= .56s

In this time, the sideways pushing magnetic force will lead to a small sideways deflection, x:

x=1/2at²

x=3x10^-9