Answer to Question #293149 in Electricity and Magnetism for Debabrata Roy

Question

b) Do the following fields satisfy all four Maxwell's equations? E(t)=E_(0)sin x sin t , B(t)=B_(0)cos x cos t

Answer 1

$\nabla \vec E=\frac \rho{ \varepsilon_0},$

$\nabla \vec B=0,$

$\nabla×\vec E=-\frac{\partial \vec B}{\partial t},$

$\nabla×\vec B=\mu_0(\vec J+\varepsilon_0\frac{\partial \vec E}{\partial t}).$