Induced currents on a pair of separated dipole antennas

[yefj]

Homework Statement

induced current from incident E-fiels

Relevant Equations

mutual impedance

Hello, I need to calculate the expression for a current on two dipoles separated as shown in the attached full task .
I need to present a solution,lets take the simplest case.
Theta_in=0

I need to find the expression for the currents on the dipoles.

https://eceweb1.rutgers.edu/~orfanidi/ewa/ch24.pdf
My E-field is in Z direction and the phase is a viarable of X.
1.What expression should i use to get the current on the dipole?

After that i opened chapter 25
https://eceweb1.rutgers.edu/~orfanidi/ewa/ch25.pdf
I see that there are expressions for mutual impedance.
2What strategy do you recommend me to use to get the current on the other dipole?
Thanks.

 

[berkeman]

Welcome to PF.

This is your schoolwork, so you need to show the Relevant Equations and your Attempt at the Solution. We do not do your homework for you.

Please show us some of your work, and please use LaTeX (see the "LaTeX Guide" link at the lower left of the Edit window). Thanks.

 

[yefj]

Hello berkerman, first of all I want to see what current is being induced on a single dipole.
So the question is what formula should I use for this purpose?
I have the following manual
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electromagnetics_II_(Ellingson)/10:_Antennas/10.11:_Potential_Induced_in_a_Dipole
from the manual formula (10.11.7)
$$\widetilde{V}_1^r = -\widetilde{\bf E}_2({\bf r}=0) \cdot \hat{\bf \theta} l_e \nonumber$$
(latex is not converting code into formula)
is the right
What is my l_e and E(r=0) given my task?
Given that this the correct formula ,How given Voc i get the induced current on a single dipole?
Thanks.

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