Charged particle passing through velocity selector

[Les talons]

Homework Statement

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?

Homework Equations

v = E/B

The Attempt at a Solution

[/B]
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?

 

[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).