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August 11th, 2017, 11:47 AM   #1
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e=2.718281828459

Euler's number...... the well-known mathematical constant. The number is related to every natural growth process....

But the what is the exact meaning of Euler's number in electromagnetism? How exactly it is used in electromagnetism? And how come it is so necessary?

I need very illustrative and INTUITIVE understanding about the use of mathematical constant e in electromagnetism....

I'll be thankful for every reply....
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August 11th, 2017, 12:56 PM   #2
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Where is it "necessary" in connection with electromagnetism?
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August 11th, 2017, 01:31 PM   #3
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The proton electron mass ratio is $\frac{e^8 - 10}{\varphi}$ with $\varphi$ the golden ratio

Last edited by Micrm@ss; August 11th, 2017 at 01:35 PM.
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August 11th, 2017, 02:24 PM   #4
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Quote:
Originally Posted by Micrm@ss View Post
The proton electron mass ratio is $\frac{e^8 - 10}{\varphi}$ with $\varphi$ the golden ratio
The proton to electron mass ratio is known to some degree of approximation. It is just coincidence that the formula given is within that approximation.
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August 11th, 2017, 04:20 PM   #5
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Quote:
Originally Posted by DesertFox View Post
Euler's number...... the well-known mathematical constant. The number is related to every natural growth process....

But the what is the exact meaning of Euler's number in electromagnetism? How exactly it is used in electromagnetism? And how come it is so necessary?

I need very illustrative and INTUITIVE understanding about the use of mathematical constant e in electromagnetism....

I'll be thankful for every reply....
you're probably thinking about complex sinousoids.

It's a common technique to represent sinosoids that have amplitude and phase as

$s(t) = A e^{j \omega t + \phi} = A e^{j 2 \pi f t + \phi}$

where $f$ is the frequency of oscillation, $A$ is the amplitude, and $\phi$ is an arbitrary phase angle.
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August 11th, 2017, 04:58 PM   #6
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Hi DesertFox,

romsek beat me to the punch, but for an illustration of the point, look here, perhaps starting on page 96 (the start of section 2-10). After this, $e$ first apperars on page 98 in equation (2-114) with a footnote to at least give a little explanation.

Again, per this post, I do not condone the availability of the contents of this textbook online, but since it is there, we might as well take advantage of it.
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August 14th, 2017, 02:44 AM   #7
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Quote:
Originally Posted by DesertFox View Post
Euler's number...... the well-known mathematical constant. The number is related to every natural growth process....

But the what is the exact meaning of Euler's number in electromagnetism? How exactly it is used in electromagnetism? And how come it is so necessary?

I need very illustrative and INTUITIVE understanding about the use of mathematical constant e in electromagnetism....

I'll be thankful for every reply....
In all honesty, it doesn't really crop up that much. When I studied EM at university, exponentials usually cropped up when looking at particular applications or problems, not when looking at the underlying theory, just because exponentials are useful in mathematics for all sorts of things.

However, the same is not true for other constants... the permittivity and permeability of free space ($\displaystyle \epsilon_0$ and $\displaystyle \mu_0$), which dictate how well electric fields and magnetic fields propagate through a vacuum, are key parameters of the theory. The speed of light in a vacuum is

$\displaystyle c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$

which can be derived directly from Maxwell's equations. It's a beautiful derivation.
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