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## Homework Statement

Between two plates (distant 4cm) there's an electric field (E = 100N/C).

A proton starts moving from the positive plate and an electron starts moving from the negative plate.

At what distance from the positive plate do they meet? (is "meet the right verb here? )

## Homework Equations

## a = qE/m ##

## v = at ##

## U = - \frac{e^2}{4\pi\epsilon_0 r}##

## U_i + K_i = U_f + K_f ##

## The Attempt at a Solution

I calculated ##U_i##.

It is ##-5.76x10^{-27} J ##.

Now,

## U_i = Kf ##

and

## Kf = \frac{1}{2} m_p v_p^2 - \frac{1}{2}m_e v_e^2##

I replace ## v = at = \frac{eEt}{m} ##

## U_i = [\frac{1}{2} e^2E^2 ( \frac{1}{m_p} - \frac{1}{m_e})] t^2 ##

## t = 6.39x10^-12 s ##

## x(t) = \frac{1}{2} at^2 ##

I obtain a very small value of x. 10^-13 or so.

There's a big difference (4 orders of magnitude) between the acceleration of the electron, that's true.

But they meet at very very very small distance from the positive plate.

Could you tell me if this is right?

Thank you so much