(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An electron at rest is released from rest and falls under the influence of gravity. In the first centimeter, what fraction of potential energy lost is radiated away?

2. Relevant equations

Lienard-Wichert potential for the electron of charge e is given by:

[tex]\phi = \frac{e}{R(1 - \beta \cdot \hat R)}[/tex]

In this case the charge is accelerated by a gravity (a = g).

3. The attempt at a solution

Reference:Electrodynamic Radiation by Marion and Heald

The problem hasn't mentioned whether the speed of the electron is relativistic.

If the speed of the electron is less than c ([itex]\beta << 1[/itex]) then [itex] R(1 - \beta \cdot \hat R) \rightarrow 0[/itex] and the potential can be written as:

[tex]\phi = \frac{e}{R}[/tex]

The accelerated field can be given as:

[tex]\vec E = \frac{e}{c^2 R^3}\left((\vec R \cdot \vec g)\vec R - R^2\vec g\right)[/tex]

I don't know how the potential energy can be calculated here. If the direction of g and R are the same, shouldn't E = 0?

I assumed a non-relativistic case here. Am I going wrong here?

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# Homework Help: Electron under gravity

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