- #1

mcano

- 4

- 0

## Homework Statement

"Two parallel plates having charges of equal magnitude but opposite sign are separated by 12cm. Each plate has a charge superficial density of 36nC/m2. A proton is launched from the negative plate to the positive plate. What is the minimum speed the proton should be launched to get to the positive plate?"

Well here's the problem, however, there are steps the teacher gave to solve, here are those

1. Express the electric field between the plates as a function of the charge superficial density (done)

2. Express the potential difference between the plates as a function of the charge superficial density(done)

3. Use the conservative nature of the electric fields and find an expression for the initial speed of the proton as a function of the charge superficial density, the distance between the plates and the speed when it gets to the negative plate.(Here is where i have problems)

## Homework Equations

from 1. we have that

[tex]

E = {\frac{\sigma}{\epsilon_{0}}}

[/tex]

from 2 we have that

[tex]

\Delta V = E.d = {\frac{d\sigma}{\epsilon_{0}}}

[/tex]

Given that the field is uniform, well, I'm considering it uniform since the size of the plates is not stated

Now, we have the kinetic energy

[tex]

K = {\frac{1}{2}}mv^2

[/tex]

and also we have the Torriceli's equation

[tex]

v_{f}^2 =v_{i}^2 + 2ad

[/tex]

## The Attempt at a Solution

Well, given the things before i know i can use the Torriceli's equation and get the expression, however i have no idea of how it would be possible to ge the relation between kinetic and electric potential energy, mostly because I'm not sure what is the equation for the electric potential energy in this exact problem, i have found many equations and my only guess is this:

Assuming that the potential energy at the positive plate (point B) is maximum and assuming that the kinetic energy in the negative plate is maximum (point A), thus at point A electric potential energy is zero

i have this,

[tex]

\Delta V =U_{B}-U_{A} = E.d = {\frac{d\sigma}{\epsilon_{0}}}

[/tex]

And given that at the point A:

[tex]

U_{A} = 0

\rightarrow U_{B} = {\frac{d\sigma}{\epsilon_{0}}}

[/tex]

Then i could do

[tex]

K = U

[/tex]

But I'm not so sure about this, so i was wondering if someone could give me a better explanation

Thanks beforehand