Motion of 2 charged particles in a constant electric field

[an_mui]

Two large parallel copper plates are 5.0cm apart and have a uniform eletric field between them as shown below. An electron is released from the negative plate at the same time that a proton is released from the positive plate. Neglect th force of the particles on each other and find their distance from the positive plate when they pass each other.

proton ->
electron <--

F = ma
Force is constant, so acceleration is proportional to 1 / m

d = distance from positive plate
1. d = 0.5a1t^2
2. d = 0.05 - 0.5 a2t^2

can someone check my progress so far? I am really stuck on this question. I am still not very good at the concept of electric field and electric potential

 

[Tide]

Looks good - now what?

 

[berkeman]

You're on the right track. The only thing different is the masses of the two particles and their +/- charge. It's just a distance versus acceleration problem.

 

[an_mui]

hm how can i solve the problem without actual numbers given in the equation?

 

[stunner5000pt]

what is the force on a charged particle q in an electric field E. Once you figure out how to write that relation you can find the accelerations taht you need.
when they pass the distance from the positive plate is equal. SO you simply equate what you have already and solve for t.
Once you have t can u use one of the kinematic equations to solve for the distnace traveled by either hte proton or the electron.

 

[an_mui]

so the force on a charged particle q in an electric field E

Fnet = eE

equation 1: 0.5(-eE/mp)t^2
equation 2: 0.05 - 0.5(eE/m)t^2

i am sorry but i still dont' know how to find the electric field.

 

[berkeman]

i am sorry but i still dont' know how to find the electric field.

You don't need to know the explicit electric field to find the answer to the question. The question just asks for the distance where the two particles pass each other. The distance is independent of the field, and only depends on the relative masses of the particles. Remember that the charge on the electron and proton is identical, just opposite in sign.

 

[stunner5000pt]

sometimes you got to keep going and try and see waht you get without knowing things at first. Perhaps they may cancel out (they probably do, here) and may not evne be required as a result. Another type of problem where somethiing apparently 'fundamental' to the problem isn ot needed is the mass of a freefalling object.

 

[an_mui]

i tried and i really can't see what step i can take next.

 

[berkeman]

Just write the two F = ma = qE equations for the two different masses, and integrate to get the distance versus time equations. Then look at the ratio to see how much farther the lighter electron gets in some time compared to the proton. The ration will likely be their relative masses or something like that. If the lighter object gets twice as far in the same time as the heavier object, then if they are moving toward each other, they will pass at the 1/3 point in their initial separation, for example.