Talk:MyOpenMath/Electromagnetic momentum

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This scrapbook is reserved for the instructor's notes to the original version of this essay.

https://en.wikiversity.org/wiki/File:E14-V20-B1.gif File:Wave_packet.gif

 
Here   is real and   has an imaginary part related to skin depth.
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Ranked from most elementary to most advanced: Phasor algebra MyOpenMath/Complex phasors w:Poynting's theorem w:Poynting_vector w:Maxwell_stress_tensor




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List of equations in table

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For future reference and editing:

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  •   intensity = power/area
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Removing discussion about dimensional analysis

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Complicated calculations should always begin with an effort to reduce the number equations and symbols involved. We begin with the six expressions shown the table. Electric conductivity,  , appears in the expression,

 ,

 

 

 

 

(1)

where   is the exponential damping rate, which is measured in inverse-seconds. One reason to deemphasize   is that it is not expressed in one of the seven SI base units. We remove   from the force equation as follows:

 ,

 

 

 

 

(2)

where,

 

 

 

 

 

(3)

is the Poynting vector. While it may seem more natural to express the force density in terms of current and magnetic field, as  , the bother of trying to remember   in (2) as some constant time conductivity, is rewarded by the simplicity of verifying that the units check. Using the textbooks notation, we use square brackets   to denote dimensions, with   denoting (length, mass, time.) To obtain the dimensions of the LHS of (2), use the fact that force density,  , is force,  , per unit volume:

 

 

 

 

 

(4)

Turning our attention to the RHS of (2), we first note that  . The Poynting vector vector,   equals the electromagnetic power that flows through a unit area. Energy,  , has the same units as work (force X distance) and, power,  , is the time derivative of energy. Therefore:

 

 

 

 

 

(5)

We shall soon see that with (4), the variable for conductivity   can be effectively removed from consideration.

Put this somewhere in an introduction

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It is not customary to model a transverse electromagnetic wave in a conductor using a real-valued wavenumber and a complex angular frequency. Usually the wave is usually created the system with a real frequency and calculating the decay with respect to distance into the medium, as shown in the figure. The driving (real-valued) frequency might be created by microwaves or an ac voltage source. We adopt this unorthodox model because the mathematical solution was stated in OpenStax Physics as the solution to the damped harmonic oscillator.

Fun modification of lorem ipsum

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Homework assignment
Replace Lorem ipsum with an abstract and introduction to this essay.

Non levis momentum habent?

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Examinatin electricae atque magneticae in wiki vniuersitatis.

Ac momentum habent ordinem per impulse:

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