# Nonuniform Acceleration - Radio Waves Effect on Ionosphere Electron

1. Dec 20, 2013

### Inklings

Hi,

Reading through an Introductory Mechanics Textbook, I don't understand a part of an example on Nonuniform Acceleration - The effect of a Radio Wave on an Ionosphere Electron.

a0 = (-eE0/m)sinÏ‰t

By my reasoning,

since at t=0, sinÏ‰t = sin0 = 0
âˆ´ a0 = 0

Sofia :)

Last edited: Dec 20, 2013
2. Dec 20, 2013

### Staff: Mentor

I don't see the link. Maybe try again?

3. Dec 20, 2013

### cepheid

Staff Emeritus
Welcome to PF Inklings (or Sofia, actually!),

There is no link attached. I will make some assumptions about what is going on in your example. If the electric field is given by the function:

E(t) = E0sinÏ‰t

Then, the acceleration is F/m = (qE)/m, where q is the charge that the field is acting on. In the case of an electron, q = -e, and we have for the acceleration as a function of time:

a(t) = -eE/m = (-eE0/m)sinÏ‰t

Now, we know that under a sinusoidal force, the acceleration will be sinusoidal as well, so we can write it in the general form a(t) = a0sinÏ‰t where a0 is the amplitude. *By comparison* with the expression for a(t) above, we conclude that a0 = (-eE0/m).

This makes sense. The amplitude (max value in either direction) of the acceleration is just the amplitude (max value) of the force, divided by the mass.

The problem in your original post was that you mistakenly had the factor of sinÏ‰t in your expression for a0.