August 11th, 2017, 10:47 AM  #1 
Member Joined: Jul 2017 From: europe Posts: 51 Thanks: 0  e=2.718281828459
Euler's number...... the wellknown 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.... 
August 11th, 2017, 11:56 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,546 Thanks: 1754 
Where is it "necessary" in connection with electromagnetism?

August 11th, 2017, 12:31 PM  #3 
Senior Member Joined: Oct 2009 Posts: 519 Thanks: 165 
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 12:35 PM. 
August 11th, 2017, 01:24 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,589 Thanks: 612  
August 11th, 2017, 03:20 PM  #5  
Senior Member Joined: Sep 2015 From: USA Posts: 2,105 Thanks: 1093  Quote:
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.  
August 11th, 2017, 03:58 PM  #6 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 626 Thanks: 90 Math Focus: Electrical Engineering Applications 
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 210). After this, $e$ first apperars on page 98 in equation (2114) 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. 
August 14th, 2017, 01:44 AM  #7  
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,127 Thanks: 716 Math Focus: Physics, mathematical modelling, numerical and computational solutions  Quote:
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.  