# Uniform electric field moving a proton and electron

• gsquare567
In summary, a proton and an electron are released from opposite ends of two parallel plates with a uniform electric field of 640 N/C between them. The question asks for the distance from the positive plate where the two particles will pass each other. By using the equations for position and force, it is determined that the particles will not meet in the middle because they have different masses and therefore different accelerations. However, their combined distances from the positive plate will add up to 4.00 cm.
gsquare567

## Homework Statement

A uniform electric field of magnitude 640 N/C exists between two parallel plates that are 4.00 cm apart. A proton is released from the positive plate at the same instand that an electron is released from the negative plate. Determine the distance from the positive plate that the two pass each other. (Ignore the electrostatic attraction between the proton and electron.)

r = 0.04 m
E = 640 N/C
qp = 1.6 * 10-19 C
qe = -1.6 * 10-19 C
mp = 1.67 * 10-27 kg
me = 1/1830 * mp

## Homework Equations

[1] x = x0 + v0 + 1/2*a*t2
[2] F = ma = qE

## The Attempt at a Solution

PROTON:
using [2], a = qp*E/mp
subbing into [1], xp = 1/2(qp*E/mp)t2

ELECTRON:
xe = r + 1/2(qe*E/me)t2

see when xp = xe
t = $$\sqrt{2*r/(E(qp/mp - qe/me}$$
i get t = 2.67 * 10-8 seconds

but when i plug it in for xp i get 2.18*10-5 m, whereas xe is 4.00 * 10-2 m

they should be equal =S

where did i go wrong? thanks!

Should they be equal? Does equal force imply equal acceleration in this case?

I thought they would be different because a proton has 1830 times the mass of an electron, and as F = m * a... Am I wrong?

No, no, you're right in that. They won't meet in the middle, though, because they've been accelerated unequally. You want not xp = xe, but xp + xe = 4.

Oh, I understand what you mean now. However, they are released from opposite ends, so I think when they cross, their x values should be equal. That is why my x equation for the electron starts at r = 4.

If one particle starts at 0, and the other at r = 4, then one will accelerate in the positive r direction, and the other will accelerate in the negative x direction.

## What is a uniform electric field?

A uniform electric field is a region in space where the electric field strength is constant. This means that the electric field lines are parallel and evenly spaced.

## How does a uniform electric field affect a proton and an electron?

In a uniform electric field, both a proton and an electron will experience a force in the direction of the electric field. The magnitude of the force will depend on the charge of the particle and the strength of the electric field.

## What is the direction of the force experienced by a proton and an electron in a uniform electric field?

The force experienced by a proton and an electron in a uniform electric field will be in the direction of the electric field. This means that for a positive charge, the force will be in the same direction as the electric field, while for a negative charge, the force will be in the opposite direction.

## How does the acceleration of a proton and an electron in a uniform electric field compare?

The acceleration of a proton and an electron in a uniform electric field will be different due to their different masses. However, the ratio of their accelerations will be equal to the ratio of their charges. This means that the electron will experience a greater acceleration than the proton.

## Can a uniform electric field cause a proton and an electron to reach the same velocity?

No, a uniform electric field cannot cause a proton and an electron to reach the same velocity. This is because their masses are different, and the acceleration of each particle is dependent on its mass. However, they can have the same kinetic energy if they have the same velocity and different masses.

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