Answer to Question #88146 in Classical Mechanics for Nicolene Hall

Question

A particle of mass m and charge q is moving along the x-axis with
speed u when it passes between two charged parallel plates. The plates generate a uniform
electric field E_0 j in the region 0 ≤ x ≤ b and no field elsewhere. Find the angle through which the particle is deflected by its passage between the plates.

Answer 1

Force, applied to the particle:

$F = q E_0$

Force parallel to the y-axis.

Acceleration of the particle:

$a = a_y = \frac{F}{m} = \frac{qE_0}{m}$

Time of passing this region with electric field:

$t = \frac{b}{u}$

Speed of the particle in y-direction

$u_y = a_y \cdot t = \frac{ q E_0 b}{mu}$

Therefore, angle of deflection:

$\tan \theta = \frac{u_y}{u}=\frac{ q E_0 b}{mu^2}$