Sinusoidal Electromagnetic Radiaton

Made and claimed by Ida De Vierno

Short Description of Topic

]==The Main Idea==

State, in your own words, the main idea for this topic Sinusoidal is a mathematical curve that describes a smooth repetitive oscillation (think the sin curve). This topic covers how a charge can be moved sinusoidally and how it will continuously emit radiation. By observing a charge moving sinusoidal we can find the amplitude, period, frequency, wavelength and speed which we will soon discuss.

Electric Field of Capacitor http://www.monzir-pal.net/Instrumental%20Analysis/Lectures/Lecture%201-20/Lect_1_files/image001.gif

Electromagnetic Radiation

When a charge initially begins accelerating, it will take time before we can observe this change in field. When we are close to the point charge, we can see the field of a moving charge whereas further away we see the field of s stationary charge. Between these two areas, is the stretched field lines in the shell which is what we know as electromagnetic radiation. When a charge experiences momentary acceleration, it emits only a brief pulse of radiation. This differs from when the charge is moved sinusoidally as the charge will emit continuous radiation.

Charge Moved Sinusoidally

Sinusoidal is a mathematic curve that describes a smooth repetitive oscillation (think the sin curve). Thus a sinusoidal acceleration takes place when the charge is moving in any oscillatory manner. The stretched field lines that were discusses early are thus continuously varying and sinusoidal. Eectromagnetic radiation occurs only at the frequency of oscillation.

When a charge is moved sinusoidally, we can find the position of charge by y=ymaxsin(wt) where w is the angular frequency in radians per second.

Will the electromagnetic radiation also be be emitted sinusoidally?

Yes. This can be proven by differentiating position to find velocity before differentiating again to find the acceleration. (Steps can be found in examples) This sinusoidal acceleration is what causes the sinusoidal electromagnetic radiation.

Amplitude

Amplitude: Height of the peak of wave perpendicular to x axis. The amplitude is also the maximum magnitude of the electric field.

Period

The sinusoidal motion results in waves that continually repeat, much like the sin curve. The period measures the amount of time it takes to complete one repeated cycle.

Frequency

Frequency measures the number of oscillations in a given time. It is therefore the inverse of the period and its unit is either seconds inverse of Hertz. Frequency is also related to angular frequent w in radians per second by f=w/2pi.

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Show that the electromagnetic radiation emitted is sinusoidally when the charge is mo

Connectedness

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History

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See also

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Further reading

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External links

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