- #1

happyparticle

- 406

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- Homework Statement
- Find ##E_0## and ##k##, ##E= E_0 \sin(k r -\omega t)## using Gauss's equation.

- Relevant Equations
- ##\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}##

##\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}##

##\vec{E}_0 k cos(kr -\omega t) = \frac{\rho}{\epsilon_0}##

##E_0 = \frac{\rho}{\epsilon_0} / k cos(kr -\omega t)##

and

##k^2 = (\arccos{\frac{\rho}{E_0 \epsilon_0}} + \omega t)/r##

I don't think it makes sense since I found ##k = \pm \frac{\omega}{c}## using

##\Delta \vec{E} = \frac{1}{c^2} \frac{\partial ^2 E}{\partial t^2}##

should I use Gauss's equation in vacuum?

Edit: Even with Gauss's equation in vacuum I don't get the same answer.

##\vec{E}_0 k cos(kr -\omega t) = \frac{\rho}{\epsilon_0}##

##E_0 = \frac{\rho}{\epsilon_0} / k cos(kr -\omega t)##

and

##k^2 = (\arccos{\frac{\rho}{E_0 \epsilon_0}} + \omega t)/r##

I don't think it makes sense since I found ##k = \pm \frac{\omega}{c}## using

##\Delta \vec{E} = \frac{1}{c^2} \frac{\partial ^2 E}{\partial t^2}##

should I use Gauss's equation in vacuum?

Edit: Even with Gauss's equation in vacuum I don't get the same answer.

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