# Homework Help: Charged particle passing through velocity selector

1. Oct 20, 2014

### Les talons

1. The problem statement, all variables and given/known data

A velocity selector uses a 64mT magnetic field perpendicular to a 28kN/C electric field. At what speed will charged particles pass through the selector undeflected?

2. Relevant equations

v = E/B

3. The attempt at a solution

Using dimensional analysis, I converted units T = kg/(s2 A), N = kg m/s2, and C = A s, and found
N/(C T) = kg m s2 A/(A s3 kg) = m/s
which would be v = E/B.
v = 28kN /(64C mT) = 4.375x105 m/s

My question is what is conceptually going on in this problem? Is the orientation of the magnetic field varying to deflect the particles?

2. Oct 20, 2014

### rude man

No, the B and E fields are both non-time-varying and uniform, in magnitude and direction.

The mag field B deflects the charges one way and the E field deflects them the opposite way. For one speed of the charges there is zero net deflection.

Mag force = qv x B and E force is qE. So v = E/B if v and B are perpendicular.

(In general, v and B must not be collinear while the E field must be perpendicular to both. Dimensional analysis can get you the answer to within a constant dimensionless coefficient only. Your answer is correct if and only if v and B are perpendicular).