A particle entering perpendicular to a uniform electric field has no force along its initial direction. Choose x along that initial velocity and y along the field. Then vx remains constant, the time inside plates of length L is t=L/vx, and ay=mqE. If uy=0, the transverse displacement is y= ½ayt2 and the exit component is vy= ayt.
The path inside the field is parabolic under the nonrelativistic uniform-field approximation. Unlike gravity, electric acceleration can reverse when the charge sign reverses and its magnitude depends on mq. Once outside the idealised plates, the particle travels straight at its exit velocity if other forces are negligible. For angled entry, retain the initial transverse component rather than setting it to zero.
Example 1
A beam has vx=2.00×106ms−1 and travels through plates 0.0400m long. Find transit time.
t=vxL=2.00×1060.0400=2.00×10−8s.
Example 2
For that time and ay=−3.00×1012ms−2 with uy=0, find y and vy.
y= ½ayt2=−6.00×10−4m; vy=ayt=−6.00×104ms−1. Negative means opposite the chosen field direction.
Watch out: In an electric field, transverse speed grows and the field does work; total speed generally increases after perpendicular entry.