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:

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