Producing a Radiative Electric Field: Difference between revisions
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===Simple=== | ===Simple=== | ||
An electron at the origin is kicked in the +x direction. At | An electron at the origin is kicked in the +x direction. At observation location (0, 0, 1), what is the direction of the radiative electric field? | ||
The radiative electric field at this location is the traverse electric field, which always has a direction opposite the direction of <math>\vec{a}_\perp</math>. Thus, <math>\vec{E}_{radiative}</math> at the observation location points in the -x direction. | |||
===Middling=== | ===Middling=== | ||
===Difficult=== | ===Difficult=== | ||
Revision as of 15:55, 18 November 2015
This page explains the relationship between measured radiative electric field and the properties of charges in a system.
Calculating Radiative Electric Field
Maintained by Charles Kilpatrick --Ck (talk) 14:18, 18 November 2015 (EST)
A Mathematical Model
The radiative electric field can be generally modeled as [math]\displaystyle{ \vec{E}_{radiative} = \frac{1}{4 \pi \epsilon_0} \frac{-q \vec{a}_\perp}{c^2r} }[/math] where q is the charge of the accelerated particle, [math]\displaystyle{ \vec{a}_\perp }[/math] is the projected acceleration, c is the speed of light and r is the distance between the charge and the observation location.
A Computational Model
The following is a vPython model of Radiative Electric Field due to an instant of acceleration (a "kick") on a charged particle.
The acceleration vector, an initial kick in the -y direction, is represented by the yellow arrow in the center. The orange arrows seen in the model represent [math]\displaystyle{ \vec{E}_{radiative} }[/math] and the cyan arrows represent the corresponding [math]\displaystyle{ \vec{B}_{radiative} }[/math] at distance r from the particle.
Examples
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Simple
An electron at the origin is kicked in the +x direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?
The radiative electric field at this location is the traverse electric field, which always has a direction opposite the direction of [math]\displaystyle{ \vec{a}_\perp }[/math]. Thus, [math]\displaystyle{ \vec{E}_{radiative} }[/math] at the observation location points in the -x direction.
Middling
Difficult
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