A small positive charge (with charge \"q\") is launched halfway between the plat

Question

A small positive charge (with charge "q") is launched halfway between the plates of a large parallel-plate capacitor. The plates are separated by a distance "d", between them is a uniform electric field "e", and the small charge is given an initial speed v0, as shown. Express all answers in "equation form", and neglect gravity. (a) Find both the vertical and horizontal components of the charge's velocity when it hits the lower plate. (b) How far will it have travelled horizontally in the time it hits the plate?

Explanation / Answer

a) horizontal velocity won't change

vx = v0

vertical

m ay = q E

ay = q e/m

y = y0 + v0y t + 1/2 a t^2

0 = d/2 - 0.5*(q e/m) t^2

t^2 = m d/( q e)

t = sqrt( m d/(q e))

so vy = - a t = -sqrt( m d/(q e)) ( q e/m)

vy = -sqrt( d q e/m)

b)

x = v0 t = v0*sqrt( m d/(q e))

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