Finding expression for instantaneous Electric field

[zak8000]

Homework Statement

hi i have been given the following electric field phasor E=(z(5)+x(10))e-jpi(y) mV/m

Mr=100
e_r=3

Homework Equations

The Attempt at a Solution

i have been able to deduce from the results above that wave is traveling in positive y direction.

intrinsic impedance = 2176 ohms from n=sqrt(M/e)
wave velocity =17x10^6 ms-1 from v=1/sqrt(M*e)
wavelength =2pi/k=2
angular frequency=kv=17pi*10^6

so to find instanteous expression for E it should be of the form:

E(y,t)=Acos(wt-ky)
E(y,t)=(z(5)+x(10))cos(17pi*10^6*t-pi*y) is this correct ? i am just confused because there are two component is the amplitude. so is this valid?
and also for the corresponding magnetic field
H=(x(5/2176)-z(10/2176))e-jpi(y) mA/m

H(y,t)=(x(5/2176)-z(10/2176))cos(17pi*10^6*t-pi*y) is this an correct expression for the corresponing magnetic field in instantaneous form?

 

[mark726]

Thank you for your question. I have reviewed your attempt at a solution and have some feedback for you.

Firstly, your deduction that the wave is traveling in the positive y direction is correct. This can be determined by the negative sign in front of the imaginary component in the electric field phasor.

Your calculations for the intrinsic impedance, wave velocity, wavelength, and angular frequency are also correct. However, your instantaneous expression for the electric field may not be entirely accurate.

Since the electric field phasor has both a real and imaginary component, it is not valid to simply use the amplitude for both components in the instantaneous expression. Instead, you will need to use the real and imaginary parts separately. The correct expression for the electric field in instantaneous form would be:

E(y,t)=(5cos(17pi*10^6*t-pi*y)+10sin(17pi*10^6*t-pi*y)) mV/m

Similarly, for the magnetic field, the correct expression would be:

H(y,t)=(5/2176cos(17pi*10^6*t-pi*y)-10/2176sin(17pi*10^6*t-pi*y)) mA/m

I hope this clarifies any confusion you may have had. Keep up the good work!