# Amplitude of an electron

Abelard

## Homework Statement

In a typical household current, the electrons in the wire may have a drift speed of 1.3×10−4 m/s. Actual household current is not a direct current, but instead is an alternating (oscillating) current. (If you have ever received an electric shock from an outlet, you have felt this rapid alternation as a painful vibration. A safe way to see the alternation is to wave your fingers rapidly in front of a fluorescent light, and observe the stroboscopic stutter-silhouette that they form.) You can model the motion of each conduction electron as simple harmonic motion, with a frequency of 60 Hz. The drift speed is the maximum speed, what the speed would build up to if the electric field were applied continually, as in the case of direct current. What is the approximate amplitude of an electron's oscillation?

1/T=f or 1/f=T

## The Attempt at a Solution

So 1/60Hz=0.1667sec = T Then period is a time of complete cycle, so 0.1667/4sec is one amplitude. Then 0.0041667sec * drift speed = 1.3e-4* 0.004167=5.42e-7 m.

## The Attempt at a Solution

Mentor
The applied electric field that is motivating the electrons is a sinusoidal function of time. Try writing the velocity as a sine (or cosine) function of time. If you do that, how would you find the position of an electron as a function of time?

Abelard
Asin(2pi*x/lambda-2pi*f*t)=y as a function of x and t. and you're not helping me yet.

Mentor
That's a formula for traveling waves. It's not what you want. There should be no dependence on distance (x) in the argument.

Have you studied simple harmonic motion?

Abelard
I supposed I did but you didn't explain why there's no distance dependence.

Abelard
Electrons have dual nature of wave and also of particle. Did you study anything about electrons and current and the fact that it moves in a zigzagging path? It's a wave as well. But if you say so, which equation are you talking about and if you know it why not put it on your pose unless you're just showing off you "intelligence."

Mentor
Electrons have dual nature of wave and also of particle. Did you study anything about electrons and current and the fact that it moves in a zigzagging path? It's a wave as well. But if you say so, which equation are you talking about and if you know it why not put it on your pose unless you're just showing off you "intelligence."

The idea is to get *you* to think about how to solve the problem and reach a solution, not to simply give you the answer. Giving you an answer now won't help you when you face similar problems on an exam.

Abelard
Fortunately it does help me.

Mentor
Fortunately it does help me.

Well, good luck with that. I wish you success.

Abelard
OK I got it. The amplitude must be 3.448e-7m. Vmax=-A*2pi*f

Abelard
I apologize for what I said since I finally got the answer.

Staff Emeritus