# Drift velocity in uniform magnetic field near charged wire

1. May 1, 2013

### Wiseman101

Problem
(a) Derive and expression (using cylindrical coordinates) for the drift velocity of a particle of mass m and charge q in a uniform vertical magnetic field B$\hat{z}$ when the particle is located at a perpindicular distance p from a long, straight vertical wire carrying a line charge density of λ.

(b) Obtain an expression for the radius p at which the drift velocity vanishes provided q and λ are of opposite sign, and verify that for λ = 10-3, electrons experience zero net drift at p = 1cm when B = 1T.

2. Relevant equations
Drift velocity v = $\frac{F×B}{qB^2}$
The electic field due to a vertical wire carrying a charge density of λ is
$\bar{E}$ = ($λ/2\piερ$)$\hat{ρ}$

3. The attempt at a solution
(a) Using the formula with F = qE i obtained the drift velocity to be
v = ($-λ/2\piεB$)$\hat{θ}$

(b) So the electron experiences is rotating in a circle and experiences a radial force F = mρω2 (where ω = drift velocity).
Then would you plug this back into the drift velocity equation to get a second drift term?
I tried this and set the total drift equal to zero. This didn't work out for the values of the charge density and radius given. Is my method correct so far? Thanks.