Calculating Deviation of a Bullet's Trajectory

[davidbenari]

Homework Statement

A bullet (3.40g) has a velocity of 160m/s perpendicular to Earth's magnetic field 5x10^-5 T . The bullet has a charge of 13.5 x 10^-9 C.With what distance will it be deviated from its trajectory after it has traveled 1.00km?

Homework Equations

##\vec{F}=q\vec{v}\times\vec{B}##

The Attempt at a Solution

The way I visualise this problem. The bullet travels in circular motion.
It's radius of motion will be given by ##R=\frac{mv}{qB}=8.05\times 10^{11} m ##
With a radius this big, after it has traveled 1km it's almost perfectly on top of the line of its initial trajectory. Because this are my answers to the problem, I'm almost 100% sure I'm not doing it right.

 

[haruspex]

With a radius this big, after it has traveled 1km it's almost perfectly on top of the line of its initial trajectory.

It's certainly a small deviation, but it is not zero and can be calculated. The trick is to calculate it in such a way that you do not completely lose precision.
Please post an equation for the deviation.