Question

A particle with charge q, mass m, and initial speed v0 in the x direction enters a region where the electric field is uniform in the x direction. How much time does it take for the particle to cross the region of length d

Answer 1

S = 1/2 Vo t + 1/2 a t^2 = d time for particle to travel distance d

F = E q force acting on particle

a = F / m = E q / m

d = Vo t + E q / (2 m) t^2

One would need to solve the quadratic equation shown to find the time t

t^2 + (2 m) / E q * V0 t - (2 m) / E q * d = 0

or t^2 + A V0 t - A d = 0 where A = (2 m) / E q