We have discussed (i) dielectric-dielectric (ii) Conductor-dielectric and (iii)

Question

We have discussed (i) dielectric-dielectric (ii) Conductor-dielectric and (iii) Conductor-free space boundary conditions. If the electric field is specified in one medium, the corresponding field across the boundary can be calculated. In this project, you will assume that medium is a dielectric or free space. The boundary is assumed to be the plane z= 0 with E, the electric field in the region z >= 0 and E2, the field in the region z 0. Furthermore, assume the electric field in region 1, is given as Ei 5a-2ay +3a You are to create Matlab user-defined function(s) that you will use to find E2 in the other medium. The inputs are the Ei that is given above, the relative permittivities, erl and er2 and the conductivities. The user should be prompted to enter the values of both the relative permittivities and conductivities. Finally, write a script/program you will use to run the functions to calculate E- EnE The program should also display the results. Make sure you test your program for all the 3 distinct cases discussed in class. Hint: Review Example MATLAB 5.2, page 209-210. Textbook

Explanation / Answer

Necessary formulas needed
// E1= Et1+En1 And E2= Et2+En2
//Et1= E/|E|= 5i- 2j+3k/sq rt (52+22+32)= 0.81 I – 0.324j+0.487 k
//Boundary conditions are Et1=Et2
E n1= /£1
£1En1- £2 En2=
Or En2=£1/£2 En1 -/£2

Matlab programing
E1= input(‘enter coefficient of vector’)
£1= input(‘enter permittivity of medium 1’)
£2= input(‘enter permittivity of medium 2’)
= input(‘enter conductivity’)
Mag E= abs (E)
Et1= rdivide (E,magE)
Et2= Et1
En1= rdivide(P, £1)
X= =£1/£2
Y= /£2
Z= X.En1
En2=Z-Y

E2=Et2+En2

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