# Electron and proton between two plates

• cseil
In summary: Now it seems you multiplied with 2 instead of dividing by 2. The distance traveled by the proton is indeed very small.
cseil

## 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

cseil said:

## 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? )
...

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?

10^-13 in what units?
No, it is not right.
Think: Forces of the same magnitude act on both particles, F=qE. And you correctly wrote that the acceleration is a=qE/m.
me=9,11x10-31kg. mp=1.67x10-27kg.
The ratio of the masses mp/me=1833. What is the ratio of the accelerations?
Again you wrote correctly, that the distance traveled by one particle is x=a/2 t2. They travel for the same time. So what is the ratio of the distances they travelled?

ehild said:
10^-13 in what units?
No, it is not right.
Think: Forces of the same magnitude act on both particles, F=qE. And you correctly wrote that the acceleration is a=qE/m.
me=9,11x10-31kg. mp=1.67x10-27kg.
The ratio of the masses mp/me=1833. What is the ratio of the accelerations?
Again you wrote correctly, that the distance traveled by one particle is x=a/2 t2. They travel for the same time. So what is the ratio of the distances they travelled?

Sorry, I forgot to say the units. 10^-13 m!

The ratio of accelerations is ##\frac{a_p}{a_e} = \frac{1}{1833} ##
The ratio of distance is the same, because t is the same.

I don't understand how to use it, though

The proton travels x distance and the electron travels 1833 x distance. The sum of their distances is 4 cm. What is the distance traveled by the proton?

Oh, ok

## 0.04 = x(1833+1) ##

x is ##2.18x10^{-5}##m.

What was my mistake then?

I could not understand what you did.

## 1. What is the definition of an electron and a proton?

An electron is a subatomic particle with a negative charge that is found in the atom's electron cloud. A proton is a subatomic particle with a positive charge that is located in the atom's nucleus.

## 2. How are electrons and protons affected by electric fields?

Electrons and protons are both affected by electric fields. Electrons are repelled by positively charged electric fields and attracted to negatively charged electric fields. Protons are attracted to positively charged electric fields and repelled by negatively charged electric fields.

## 3. What is the relationship between electrons and protons in an atom?

An atom contains an equal number of positively charged protons and negatively charged electrons, making the overall charge of the atom neutral.

## 4. How do electrons and protons behave when placed between two plates with opposite charges?

When placed between two plates with opposite charges, electrons and protons will experience a force due to the electric field. Electrons will move towards the positively charged plate, while protons will move towards the negatively charged plate.

## 5. Can the movement of electrons and protons between two plates be controlled?

Yes, the movement of electrons and protons between two plates can be controlled by adjusting the strength of the electric field or by applying an external magnetic field.

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