Bainbridge's mass spectrometer problem

[wushumaster]

1. Homework Statement

Bainbridge's mass spectrometer, shown in Fig. 28-58 (look to this link for image- http://www.cramster.com/answers-apr-08/physics/solution-posted-correctly-bainbridges-mass-spectrometer-shown-fig-28-58-separat_226944.aspx) , separates ionshaving the same velocity. The ions, after entering through slits,S1 and S2, pass through a velocityselector composed of an electric field produced by the chargedplates P and P′, and a magnetic field B perpendicular to the electric fieldand the ion path. The ions that then pass undeviated through the crossed E and B fields enter into a region where a second magnetic field B prime exists, where they are made to followcircular paths. A photographic plate (or a modern detector)registers their arrival. Show that, for the ions, q/m=E/(r*B*B prime) *=multiplication, where r is the radius of the circular orbit.
2. Homework Equations

I'm kind of lost on where to start. But, we know that qvB=mv^2/r because it is uniform circular motion...

3. The Attempt at a Solution
Not sure how to begin...
Help? Thanks!

 

[anathema]

Hello! It seems like you're having trouble getting started on this problem. Don't worry, I'm here to help guide you through it.

First, let's break down the formula that we need to show: q/m=E/(r*B*B prime)

We know that q is the charge of the ion, m is its mass, and E is the electric field produced by the charged plates. The magnetic field is represented by B and B prime, and r is the radius of the circular orbit that the ions follow.

To start, let's look at the equation qvB=mv^2/r, which represents the force on a charged particle moving in a magnetic field. We can rearrange this equation to solve for v, which will be useful later.

v=qBr/m

Now, let's think about what happens to the ions as they enter the velocity selector. The electric field produced by the charged plates will exert a force on the ions, causing them to accelerate. This acceleration will cause the ions to gain velocity, which we can calculate using the equation we just rearranged.

Next, the ions enter the magnetic field B and B prime, which will cause them to follow circular paths. This means that the force on the ions must be equal to the centripetal force, which is mv^2/r. So, we can set the two equations equal to each other and solve for r.

mv^2/r=qvB

r=qvB/mv^2

Now, let's substitute our expression for v into this equation.

r=q(qBr/m)(B)/m(qBr/m)^2

This simplifies to:

r=q^2B^2r/m^2qBr

And finally, we can cancel out the q's and rearrange to get our desired formula:

q/m=E/(r*B*B prime)

I hope this helps you get started on solving this problem. Remember, always think about the forces acting on the ions and how they affect their motion. Good luck!