Physics: What is the Poynting vector S⃗ (x,t)S→(x,t), that is, the power per unit area associated with the electromagnetic wave described in the problem introduction

What is the Poynting vector S⃗ (x,t)S→(x,t), that

Rboltonbcs

10.02.2022

$\mathbf{S^{\to} (x,t) = \dfrac{{E_o} {B_o}}{\mu_o} sin^2 (kx -wt) \hat i }$

Explanation:

Consider:

$E^{\to} =E_o \ Sin (kx - wt) \hat j$

$B^{\to} =B_o \ Sin (kx - wt) \hat k$

The equation for the Poynting vector is given as:

$S^{\to} (x,t) = \dfrac{E^{\to}\times B^{\to}}{\mu_o}$

$S^{\to} (x,t) = \dfrac{E_o \ Sin(kx - wt) \hat j \times B_o sin (kx -wt) \hat k}{\mu_o}$

$S^{\to} (x,t) = \dfrac{{E_o} {B_o}}{\mu_o} sin^2 (kx -wt) (\hat j \times \hat k)$

$S^{\to} (x,t) = \dfrac{{E_o} {B_o}}{\mu_o} sin^2 (kx -wt) \hat i$

∴

$\mathbf{S^{\to} (x,t) = \dfrac{{E_o} {B_o}}{\mu_o} sin^2 (kx -wt) \hat i }$

0,0(0 оценок)