Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; JCommentsACL has a deprecated constructor in /var/www/astarmathsandphysics/components/com_jcomments/classes/acl.php on line 17 Call Stack: 0.0000 361248 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0455 1211448 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0455 1211448 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1201 4085056 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1217 4112816 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1226 4130528 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1226 4147536 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1234 4155272 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1234 4155272 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1712 4579912 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1736 4665464 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1742 4686392 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.3822 9786184 13. JEventDispatcher->trigger() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:199 0.3825 9786584 14. plgContentJComments->update() /var/www/astarmathsandphysics/libraries/joomla/event/dispatcher.php:160 0.3825 9786584 15. plgContentJComments->onContentAfterDisplay() /var/www/astarmathsandphysics/libraries/joomla/event/event.php:70 0.3827 9794832 16. plgContentJComments->onAfterDisplayContent() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:339 0.3829 9796528 17. JComments::show() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:282 0.3836 9829616 18. JCommentsFactory::getACL() /var/www/astarmathsandphysics/components/com_jcomments/jcomments.php:188 0.3836 9830016 19. spl_autoload_call() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274 0.3837 9830096 20. JLoader::load() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274
The Electromagnetic Wave Equation
We can use Maxwell's equations to derive the wave equation that electromagnetic waves obey.
We start from the equation
Substitute into this the equation
rearranged to give
and the equation
We obtain
We take the curl of both sides of this equation to obtain

Assuming
and
to be constant allows us to write

Now use the vector identity
to obtain

Free space has no charge so
to give
A similar procedure can be followed to obtain
These are both wave equations, with the wave speed give by
In a vacuum
and
They are given the symbols
and
respectively. In other materials
This means that the speed of electromagnetic radiation is less in these materials.
Add comment