Producing a Radiative Electric Field

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.

3d Radiation vPython Model

The acceleration vector, an initial kick in the +x 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

Simple

An electron at the origin is kicked in the -y direction. At observation location (0, 0, 1), what is the direction of the radiative electric field?

The radiative electric field at this location is known as 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 +y direction.

Connectedness

1. How is this topic connected to something that you are interested in?

This topic relates to my personal interest in using modelling to enhance understanding. In the past, data such as the changes over time in large, complex data sets (e.g. the knowledge base for intelligent agents) has been extremely cumbersome and borderline unintelligible without an effectively modeled rendition of this data. In the 60's, much research was done at the University of Utah in the field of computer-generated graphics, resulting in an outpouring of 3d-modelling applications, which in turn led to the invention of iconic modelling software such as Autodesk that researchers use worldwide today. As you can see, the model of the radiative [math]\displaystyle{ vec{E} }[/math] and [math]\displaystyle{ vec{B} }[/math] fields provided above greatly clarifies the nature of the change in these fields over time and offers us an interactive three-dimensional perspective on something that could only be drawn statically on whiteboards in the past.

1. How is it connected to your major?

As a computer science student in the Media thread, radiative effects are integral to modeling and animating light sources. Luminance, or the total light present in a space, is generated according to an integral of vectors over [math]\displaystyle{ k }[/math], all possible outward direction vectors from the light source. As the vectors representing the rays of light expand outward, they will interact with physical objects to create shadows, or other lights to create more intense or different-colored light. This is similar to how the [math]\displaystyle{ vec{E} }[/math] and [math]\displaystyle{ vec{B} }[/math] fields may change and distort upon interacting with other fields as they extend outward.

1. Is there an interesting industrial application?

Most practical

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See also

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