Question

The electric field of a plane standing electromagnetic wave in a vacuum is given by Ey- Eosin(kx)cos(ot). What is the corresponding expression for the magnetic field? Bz =-cos(kx)sin(at) B B cos(kox)cos(ot) Bz-sin(kx)cos(ot) Bz cos(kx)sin(at) E)Bz-sin(kx)cos(at) C) Eo

Answer 1

Answer:

$B=-\dfrac{E_o}{c}cos(kx)sin(\omega t)\ k$

Explanation:

The electric field of a plane standing electromagnetic wave in a vacuum is given by :

$E_y=E_o\ sin(kx)cos(\omega t)$

We need to find the corresponding expression for the magnetic field. According to equation of Maxwell's :

$\bigtriangledown \times E=-\dfrac{\partial B}{\partial t}$

$\bigtriangledown \times E=\begin{vmatrix}i & j & k\\ \dfrac{\partial}{\partial x} & \dfrac{\partial }{\partial y} & \dfrac{\partial}{\partial z}\\ 0& E_o\ sin(kx)cos(\omega t) & 0 \end{vmatrix}$

$\bigtriangledown \times E=k[E_ok\ cos(kx)cos(\omega t)]=-\dfrac{\partial B}{\partial t}$

$B=\int\limits {kE_ok\ cos(kx)cos(\omega t).dt}$

$B=-\dfrac{E_ok}{\omega}cos(kx)sin(\omega t)$

Since, $\omega=ck$

$B=-\dfrac{E_o}{c}cos(kx)sin(\omega t)\ k$

So, the corresponding expression for the magnetic field is $-\dfrac{E_o}{c}cos(kx)sin(\omega t)\ k$. Hence, this is the required solution.