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Using the One Dimensional Wave Equation to Represent Electromagnetic Waves in a Vacuum
Using the One Dimensional Wave Equation to Represent Electromagnetic Waves in a Vacuum
The differential wave equation can be used to describe electromagnetic waves in a vacuum. In the one dimensional case, this takes the form $\frac{\partial^2\phi}{\partial x^2}-\frac{1}{c^2}\frac{\partial^2\phi}{\partial t^2} = 0$. A general function $f(x,t) = x \pm ct$ will propagate with speed c. To represent the properties of electromagnetic waves, however, the function $\phi(x,t) = \phi _0 sin(kx-\omega t)$ must be used. This gives the Electric and Magnetic field equations to be $E (z,t) = \hat{x} E _0 sin(kz-\omega t)$ and $B (z,t) = \hat{y} B _0 sin(kz-\omega t)$. Using this solution as well as Maxwell's equations the relation $\frac{E_0}{B_0} = c$ can be derived. In addition, the average rate of energy transfer can be found to be $\bar{S} = \frac{E_0 ^2}{2 c \mu _0} \hat{z}$ using the poynting vector of the fields.
Eric Minor
Resolucion pregunta 2 del parcial de osman
Resolucion pregunta 2 del parcial de osman
trabajo realizado para la cátedra de señales y sistemas
Josue Maldonado
Math 333 Weekly Homework Template
Math 333 Weekly Homework Template
This is a template for students from Math 333 at Hood College to use for weekly homework submission. (Fall 2018)
Jill Tysse
Math 392A Overleaf Form
Math 392A Overleaf Form
HoTT
Parikshit Khanna
Càlcul 1. Parcial 2014p
Càlcul 1. Parcial 2014p
Solucions del parcial del día 9/4/2015.
Jordi Saludes
Real Analysis I (Workshop 2)
Real Analysis I (Workshop 2)
Real Analysis Workshop 2 1.3.10
Philip Mak
E5: Kern- und Teilchenphysik Übungsblatt 6
E5: Kern- und Teilchenphysik Übungsblatt 6
Übungsblatt 6
Jean Amadeus Elsner
Ejercicio 11 del 78, Baldor
Ejercicio 11 del 78, Baldor
Resuelva la ecuación
Wilson

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