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Old Aug 11th 2017, 12:34 PM   #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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Old Aug 11th 2017, 02:00 PM   #2
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I'll be thankful for every reply....
Well you didn't reply to my description of affine geometry I made for you elsewhere !
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Old Aug 11th 2017, 02:28 PM   #3
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Every exponential can be written in terms of e: $\displaystyle a^x= e^{ln(a^x)}= e^{x ln(a)}$ so anywhere there is an exponential to any base, we can use "e". $\displaystyle e^x$ happens to have the nice property that its derivative is itself: $\displaystyle \frac{de^x}{dx}= e^x$.

Last edited by HallsofIvy; Aug 14th 2017 at 10:28 AM.
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Old Aug 11th 2017, 10:56 PM   #4
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Are you perhaps confusing E, the electric field vector, with e which is euler's number? They are not the same thing.
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Old Sep 17th 2017, 10:37 PM   #5
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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?
Why are you saying that its so necessary? In what context are you referring to it being used?

e is the base of the natural logarithm I believe it appears when analyzing the decrease in the amplitude of an EM wave when it enters a material.

Also, all EM waves can be described using sinusoidal waves (e.g. in terms of Fourier integrals of Fourier series) which use the sine and cosine functions. Those functions can be written in terms of e by using Euler's formula: See: https://en.wikipedia.org/wiki/Euler%27s_formula

It can make the math easier when expressed in terms of e.
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