Answer to Question #97793 in Electrical Engineering for Aparna

Question

1. Consider a cube with dimension (1 m)x (1 m) x (1 m). It is anchored at the spatial origin and point (1,1, m. All of its faces are parallel to the Cartesian axes, as shown in cube . This cube is filled with air, and all of its six faces are made of perfect electric conductor. There is no source within the cube and the electric field (in phaser form ) within the cube is
E(Y,Z)=X^sin(2pi y) sin(2pi z) (V/m)
1. What is angular frequency omega
2.what is time dependent expression of the electric field

Answer 1

1) First, calculate the propagation constant:

$$k=\sqrt{k_y^2+k_z^2}=\sqrt{(2\pi)^2+(2\pi)^2}=8.886\text{ rad/m}.$$

The angular frequency:

$$\omega=kc=8.866\cdot2.666\cdot10^9\text{ rad/s}.$$

2) The time-dependent expression:

$$\bold{E}=E(y,z)e^{i\omega t}=\hat{x}\text{ sin}(2\pi y)\text{ sin}(2\pi z)\cdot e^{2.666\cdot10^9it}.$$