# Electrostatic Potential

## Homework Statement

Two parallel plates are positioned horizontally and when the potential te?difference between the plates is 400 V, a charged particle is suspended freely 10 cm above the lower plate. If the potential difference is suddenly changed to 200 V, how long will it take the particle to reach the lower pla

-dV/dr=E
U=qV
V=kq/r

## The Attempt at a Solution

If the difference between Va and Vb=400 V,

1. 400=kq/r
q=4.44 x 10^-9

2. U=qV, V=200
U=8.89 x 10^-7

3. U=KE

Since there's no mass, this is where I got stuck. Honestly, I've looked at this problem several different ways, and I just really don't understand electric potential well enough to know if what I'm doing even makes sense. Any feedback would be appreciated.

kuruman
Homework Helper
Gold Member
First off, V = kq/r is the potential for a point charge. This is not what you have here. Here the electric field between the parallel plates is constant, so the potential difference over distance d is given by V = E d, where E is the (constant) electric field between the plates.

Can you find an expression for the mass in terms of the other parameters if you know that the charged particle is suspended freely when V = 400 Volts?

Okay, so if I understand what you're saying, mg=Fcoulomb, and we should be able to get Fcoulomb from E(q)? How do we get q if V=kq/r is for a point charge? Basically, I don't remember finding V for parallel plates. Am I on the right track yet, though?

kuruman