# Inf. Parallel Plate Capacitors and Potential Energy

1. Mar 13, 2015

### kevtimc25

Hopefully no one minds that I post a couple questions in a row as long as I'm following the rules:

1. The problem statement, all variables and given/known data

Two infinite parallel plates labelled W and X are separated by 5.2 cm. The electric potential between the plates is 150 V. An electron starts from rest at time tW and reaches plate X at time tX. The electron continues through the opening and reaches point P at time tP

c.) Find the electron’s kinetic energy and potential energy at point *P.
d.) Find the minimum speed of the electron at time tw needed for it to escape to infinity.

2. Relevant equations
U = qV , energy conserved

3. The attempt at a solution
We can calc. the KE X easily: Ux = 0, Ex = Uw, Uw = 150V * -1.60*10^-19 C = 1/2 m(e) v^2 so we have v and there is no electric field once it is outside of the plates. A previous given answer indicates that the speed is constant once we hit X (I don't understand why other than that no outside forces are acting on the electron if we exclude gravity), so how can we calculate U and K at *P?

2. Mar 14, 2015

### Simon Bridge

Do we know the initial position of the electron?
If the electron is accelerated through a potential difference of V then it's kinetic energy is V electron-volts.

Per your question: do you know how to calculate the potential due to a single plate?
Do you know the superposition principle?

3. Mar 14, 2015

### kevtimc25

Yes it is at rest at W.

I know the EF is σ/2e0 everywhere due to each plate and you can find V by integrating E through a distance. And I know you can also find V by adding the potentials from each plate. But we don't now the Surface density of the plates.

4. Mar 14, 2015

### Simon Bridge

You also know the potential difference between the plates is 150V... this gives you the kinetic energy at X.
Per the charge density - just put it equal to $+\sigma$ for the +ve plate and $-\sigma$ for the -ve plate.

5. Mar 14, 2015

### kevtimc25

Right, outside of the PPC the EF is 0 everywhere, so the ΔV would have to be 0 right? That means the potential doesn't change so the KE can't change as well (at point X and beyond).