Two large parallel conductive plates are 5 cm apart and have a uniform electric

Question

Two large parallel conductive plates are 5 cm apart and have a uniform electric field between them. An electron is released from rest from the negative plate at the same time that a proton is released from rest from the positive plate. Neglect the force of the particles on each other (assume they are very far from each other laterally), find their distance from the positive plate when they pass each other. Note the mass of the proton is 1833.15 times greater than the mass of the electron. Neglect the effect of gravity.

Explanation / Answer

here

F = q *E = m *a

x(t) = x0 + 0.5 * a *t^2 = x0 + 0.5 * q *E / m t^2

for the proton

xp(t) = 0.5 *( q *E / mp ) t^2

t^2 = xp * mp * 2 / q*E

for the electron

xe(t) = d - 0.5 *( q *E / me) * t^2

t^2 = (d - xe) * 2 * me / q*E

at the time they pass xp = xe

xp * mp * 2 / q *E = (d -xp) *2 * me /q*E

xp * mp = d* me - xp *me

xp( mp + me ) = d *me

xp = d * me / ( mp + me)

here the mass of the proton is 1833.15 time greater than the mass of the electron

therefore the   mp = 1833.15 * me

xp = d * me / ( 1833.15 * me + me)

xp = 0.05 / 1834.15

xp = 2.72 * 10^-5 m

so the distance form the postive plate is 2.72 * 10^-5 m

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