Friday 7-18-96
This is discussed in the mass spectrometer section of 18.5
One application of a velocity selector is as the first stage in a mass spectrometer. A velocity selector is designed to allow charges (usually ions) of only a particular velocity to pass through undeflected. Slower charges will generally be deflected one way, while faster charges will deflect another way. The velocity selector uses both an electric field and a magnetic field, with the fields at right angles to each other, as well as to the velocity of the incoming charges.
Imagine the case of positively-charged ions moving from left to right on the page, and an electric field pointing down the page. This will tend to deflect the ions down the page with a force of F = qE. Now, add a magnetic field pointing into the page. By the right hand rule, this gives a force of F = qvB which is directed up the page. Note that the magnetic force depends on the velocity, so there will be some particular velocity where the electric force qE and the magnetic force qvB are equal and opposite. Setting the forces equal, qE = qvB, and solving for this velocity gives v = E/B. So, a charge of velocity v = E/B will experience no net force, and will pass through the velocity selector undeflected.
A charge moving slower than this will have the magnetic force reduced, and will bend down the page, in the direction of the electric force. A charge moving faster than this will have a larger magnetic force, and will bend up the page, in the direction of the magnetic force.
The above arguments can be extended to negative charges, the only difference being that the forces would simply be in the opposite direction to the way they are for positive charges.