Question

A mass spectrometer similar to the one in the figure below is designed to separate protein fragments. The fragments are ionized by removing a single electron and then enter a 0.70 T uniform magnetic field at a speed of 2.0 105 m/s. If a fragment has a mass 90 times the mass of the proton, what will be the distance between the points where the ion enters and exits the magnetic field?

https://imgur.com/a/6JzFK

Answer 1

Once the protein fragment is ionized (i.e. loses ONE electron) its electric charge will be

  

The magnetic force exerted on the protein ion when it enters the mass spectrometer is given by:



Where


(Protein ion's velocity)

B = strength of the magnetic field = 0.70 T

The situation simplifies because the direction of the magnetic field and velocity are perpendicular.

But we also note that the magnetic force is balanced by the centripetal force of the particle traveling IN A CIRCLE:

v = velocity = 2.0 x 10^5 m/s
r = radius of ion's path

When we equate the two forces we get:



or



But the distance from the entrance of the ion to the point where it exits the magnetic field is 2*r (the DIAMETER of the circle is makes). Therefore:

or 53cm
so

So the answer is that the particle will exit the magnetic field 0.53m from where it entered.