A plane electromagnetic wave moving through free space has an E- field given by E_x=0; E_y=0; E_z=100 sin[8π×〖10〗^14 (t- x/(3×〖10〗^8 ))]. Calculate the corresponding flux density.

To calculate the corresponding flux density, also known as the electromagnetic wave intensity or power density, we need to use the formula:

I = 0.5 * ε₀ * c * E²

where:
I is the intensity or flux density
ε₀ is the permittivity of free space, approximately 8.854 × 10⁻¹² F/m
c is the speed of light in vacuum, approximately 3 × 10⁸ m/s
E is the electric field amplitude of the wave

Given that the electric field components are E_x = 0, E_y = 0, and E_z = 100 sin[8π×10¹⁴ (t- x/(3×10⁸))], we can calculate the corresponding flux density.

First, let's find the amplitude of the electric field, E:

E = √(E_x² + E_y² + E_z²)
= √(0² + 0² + (100 sin[8π×10¹⁴ (t- x/(3×10⁸))])²)
= √(100 sin[8π×10¹⁴ (t- x/(3×10⁸))])²)
= 100 sin[8π×10¹⁴ (t- x/(3×10⁸))]

Now, we can substitute the values into the formula to calculate the flux density, I:

I = 0.5 * ε₀ * c * E²
= 0.5 * (8.854 × 10⁻¹² F/m) * (3 × 10⁸ m/s) * [100 sin[8π×10¹⁴ (t- x/(3×10⁸))]]²

Finally, we simplify the expression and calculate the value of I for any given values of t and x.