Question

An electromagnetic wave in free space has an electric-eld vector E = f(t - z/c0).x, where ^x is a unit

vector in the x direction, and f(t) = e^-t^2=2

e^j2pv0t, where y is a constant. Describe the physical nature

of this wave and determine an expression for the magnetic-eld vector.

Answer 1

Gives

$E=f(t-\frac{z}{c_0})\hat{x}$

$f(t)=e^{-t^2},y=2e^{j2\pi v_0t}=2e^{jwt}$

We know that wave equation

$y=Ae^{(jw_0t+\phi)}$

Where A=amplitude

$w_0=$ Anguler frequency

$\phi$ =phase

$y=2e^{j2\pi v_0t}=2e^{jwt}\rightarrow(1)$

equation (1) is showing wave equation

equation (1)is

Phase

$\phi$ =0°

Amplitude=2

Anguler frequency

$w=2\pi v_0$

Magnetic field vector

$B=\frac{E}{c}$

$B=\frac{E}{c}=\frac{f(t-\frac{z}{c_0})\hat{x}}{c}$

Where

$f(t)=e^{-t^2}$