Question

Two parallel plates, each charged equally and oppositely to the other, are separated by 3.5000 cm. A proton is let go from rest at the positive plate's surface and, at the same time, an electron is let go from rest at the negative plate's surface. What is the distance between the negative plate and the point where the proton and the electron go by each other?

This one will need your answer correct to 5 significant digits

Answer 1

Both protons and electrons feels same force, which is

F = q*E = e*E

But they experience different acceleration

a = F/M

distance moved by electron will be

de = u*te + 0.5*ae*te^2

u = 0, ae = F/Me,

de = 0.5*e*E*te^2/Me

Similarly for proton

dp = 0.5*e*E*tp^2/Mp

Since when they cross

tp = te

So

de*Me = dp*Mp

de = d - dp

(d - dp)*Me = dp*Mp

dp = d*Me/(Me + Mp)

dp = 3.5000*10^-2*9.1*10^-31/(9.1*10^-31 + 1.67*10^-27)

dp = 1.9061*10^-5 m

de = d - dp = 0.035000 - 1.9061*10^-5

de = 3.4980*10^-2 m = 3.4980 cm