Answer to Question #88146 in Classical Mechanics for Nicolene Hall

Question #88146
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.
1
Expert's answer
2019-04-17T11:13:23-0400

Force, applied to the particle:


F=qE0F = q E_0

Force parallel to the y-axis.

Acceleration of the particle:


a=ay=Fm=qE0ma = a_y = \frac{F}{m} = \frac{qE_0}{m}

Time of passing this region with electric field:


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

Speed of the particle in y-direction


uy=ayt=qE0bmuu_y = a_y \cdot t = \frac{ q E_0 b}{mu}

Therefore, angle of deflection:


tanθ=uyu=qE0bmu2\tan \theta = \frac{u_y}{u}=\frac{ q E_0 b}{mu^2}


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