![Considers applying the boundary conditions on the boundary between two different media.
Considering er1=2 and er2=3
Use the given MATLAB code that's provided with question to calculate the following fields:
% This script allows the user to enter an electric field
% on either side of a dielectric boundary and compute the
% electric field on the other side of the boundary
%
% The boundary is assumed to be the plane z=0, with E1 the field in
% the region z >=0 and E2 the field in the region z <= 0
%
% inputs: E1 or E2, er1 and er2 (the relative permittivities of both media
% outputs: E1 or E2, the field not input by the user
clear
% prompt user for input materials
er1 = input('Enter the relative permittivity in the region z > 0... > ');
if isempty(er1); er1 = 1; elseif er1 < 1; er1 = 1; end % check if dielectric is physical
er2 = input('Enter the relative permittivity in the region z < 0... > ');
if isempty(er2); er2 = 1; elseif er2 < 1; er2 = 1; end % check if dielectric is physical
% prompt the user for the region
side = input('Enter the side of the interface where the electric field is known (given)... > ');
% if user entered something other than "r" "c" or "s" set default as "r"
if isempty(side); side = 1; elseif side > 2; side = 2; end % check if dielectric is physical
if side == 1;
% prompt the user for the field
E1 = input('Enter the electric field in side 1 in the form [Ex Ey Ez]... >');
E1n = E1(3)*[0 0 1]; % normal direction is +z
E2n = E1n*er1/er2; % e-field boundary condition for normal component
E1t = E1 - E1n; % tangential component of E1
E2t = E1t; % e-field boundary condition for tangential component
E2 = E2t + E2n;
elseif side == 2;
% prompt the user for the field
E2 = input('Enter the electric field in side 2 in the form [Ex Ey Ez]... >');
E2n = E2(3)*[0 0 1]; % normal direction is +z
E1n = E2n*er2/er1; % e-field boundary condition for normal component](https://image.slidesharecdn.com/considersapplyingtheboundaryconditionsontheboundarybetweent-230327052338-31dccba3/85/Considers-applying-the-boundary-conditions-on-the-boundary-between-t-pdf-1-320.jpg)
![E2t = E2 - E2n; % tangential component of E2
E1t = E2t; % e-field boundary condition for tangential component
E1 = E1t + E1n;
else
disp('Invalid specification, please re-try ');
end
% Display results
disp(sprintf('The electric fields are E1 = (%d, %d, %d) V/m E2 = (%d, %d, %d) V/m',...
E1(1), E1(2), E1(3), E2(1), E2(2), E2(3))) 1- E2 given that E1 - 3ax + 4ay + 5a, 2- E1 given
that E2 -3ax + 4ay 5az
Solution
matlab result:
>> electricboundary
Enter the relative permittivity in the region z > 0...
> 2
Enter the relative permittivity in the region z < 0...
> 3
Enter the side of the interface where the electric field is known (given)...
> 1
Enter the electric field in side 1 in the form [Ex Ey Ez]...
>[3 4 5]
The electric fields are
E1 = (3, 4, 5) V/m
E2 = (3, 4, 3.333333e+00) V/m
>>
for side 2:
>> electricboundary
Enter the relative permittivity in the region z > 0...
> 2
Enter the relative permittivity in the region z < 0...
> 3
Enter the side of the interface where the electric field is known (given)...
> 2
Enter the electric field in side 2 in the form [Ex Ey Ez]...](https://image.slidesharecdn.com/considersapplyingtheboundaryconditionsontheboundarybetweent-230327052338-31dccba3/85/Considers-applying-the-boundary-conditions-on-the-boundary-between-t-pdf-2-320.jpg)
![>[3 4 5]
The electric fields are
E1 = (3, 4, 7.500000e+00) V/m
E2 = (3, 4, 5) V/m
MAtlab code:
% This script allows the user to enter an electric field
% on either side of a dielectric boundary and compute the
% electric field on the other side of the boundary
%
% The boundary is assumed to be the plane z=0, with E1 the field in
% the region z >=0 and E2 the field in the region z <= 0
%
% inputs: E1 or E2, er1 and er2 (the relative permittivities of both media
% outputs: E1 or E2, the field not input by the user
clear
% prompt user for input materials
er1 = input('Enter the relative permittivity in the region z > 0... > ');
if isempty(er1); er1 = 1; elseif er1 < 1; er1 = 1; end % check if dielectric is physical
er2 = input('Enter the relative permittivity in the region z < 0... > ');
if isempty(er2); er2 = 1; elseif er2 < 1; er2 = 1; end % check if dielectric is physical
% prompt the user for the region
side = input('Enter the side of the interface where the electric field is known (given)... > ');
% if user entered something other than "r" "c" or "s" set default as "r"
if isempty(side); side = 1; elseif side > 2; side = 2; end % check if dielectric is physical
if side == 1;
% prompt the user for the field
E1 = input('Enter the electric field in side 1 in the form [Ex Ey Ez]... >');
E1n = E1(3)*[0 0 1]; % normal direction is +z
E2n = E1n*er1/er2; % e-field boundary condition for normal component
E1t = E1 - E1n; % tangential component of E1
E2t = E1t; % e-field boundary condition for tangential component
E2 = E2t + E2n;
elseif side == 2;
% prompt the user for the field
E2 = input('Enter the electric field in side 2 in the form [Ex Ey Ez]... >');
E2n = E2(3)*[0 0 1]; % normal direction is +z](https://image.slidesharecdn.com/considersapplyingtheboundaryconditionsontheboundarybetweent-230327052338-31dccba3/85/Considers-applying-the-boundary-conditions-on-the-boundary-between-t-pdf-3-320.jpg)
Considers applying the boundary conditions on the boundary between t.pdf
- 1. Considers applying the boundary conditions on the boundary between two different media. Considering er1=2 and er2=3 Use the given MATLAB code that's provided with question to calculate the following fields: % This script allows the user to enter an electric field % on either side of a dielectric boundary and compute the % electric field on the other side of the boundary % % The boundary is assumed to be the plane z=0, with E1 the field in % the region z >=0 and E2 the field in the region z <= 0 % % inputs: E1 or E2, er1 and er2 (the relative permittivities of both media % outputs: E1 or E2, the field not input by the user clear % prompt user for input materials er1 = input('Enter the relative permittivity in the region z > 0... > '); if isempty(er1); er1 = 1; elseif er1 < 1; er1 = 1; end % check if dielectric is physical er2 = input('Enter the relative permittivity in the region z < 0... > '); if isempty(er2); er2 = 1; elseif er2 < 1; er2 = 1; end % check if dielectric is physical % prompt the user for the region side = input('Enter the side of the interface where the electric field is known (given)... > '); % if user entered something other than "r" "c" or "s" set default as "r" if isempty(side); side = 1; elseif side > 2; side = 2; end % check if dielectric is physical if side == 1; % prompt the user for the field E1 = input('Enter the electric field in side 1 in the form [Ex Ey Ez]... >'); E1n = E1(3)*[0 0 1]; % normal direction is +z E2n = E1n*er1/er2; % e-field boundary condition for normal component E1t = E1 - E1n; % tangential component of E1 E2t = E1t; % e-field boundary condition for tangential component E2 = E2t + E2n; elseif side == 2; % prompt the user for the field E2 = input('Enter the electric field in side 2 in the form [Ex Ey Ez]... >'); E2n = E2(3)*[0 0 1]; % normal direction is +z E1n = E2n*er2/er1; % e-field boundary condition for normal component
- 2. E2t = E2 - E2n; % tangential component of E2 E1t = E2t; % e-field boundary condition for tangential component E1 = E1t + E1n; else disp('Invalid specification, please re-try '); end % Display results disp(sprintf('The electric fields are E1 = (%d, %d, %d) V/m E2 = (%d, %d, %d) V/m',... E1(1), E1(2), E1(3), E2(1), E2(2), E2(3))) 1- E2 given that E1 - 3ax + 4ay + 5a, 2- E1 given that E2 -3ax + 4ay 5az Solution matlab result: >> electricboundary Enter the relative permittivity in the region z > 0... > 2 Enter the relative permittivity in the region z < 0... > 3 Enter the side of the interface where the electric field is known (given)... > 1 Enter the electric field in side 1 in the form [Ex Ey Ez]... >[3 4 5] The electric fields are E1 = (3, 4, 5) V/m E2 = (3, 4, 3.333333e+00) V/m >> for side 2: >> electricboundary Enter the relative permittivity in the region z > 0... > 2 Enter the relative permittivity in the region z < 0... > 3 Enter the side of the interface where the electric field is known (given)... > 2 Enter the electric field in side 2 in the form [Ex Ey Ez]...
- 3. >[3 4 5] The electric fields are E1 = (3, 4, 7.500000e+00) V/m E2 = (3, 4, 5) V/m MAtlab code: % This script allows the user to enter an electric field % on either side of a dielectric boundary and compute the % electric field on the other side of the boundary % % The boundary is assumed to be the plane z=0, with E1 the field in % the region z >=0 and E2 the field in the region z <= 0 % % inputs: E1 or E2, er1 and er2 (the relative permittivities of both media % outputs: E1 or E2, the field not input by the user clear % prompt user for input materials er1 = input('Enter the relative permittivity in the region z > 0... > '); if isempty(er1); er1 = 1; elseif er1 < 1; er1 = 1; end % check if dielectric is physical er2 = input('Enter the relative permittivity in the region z < 0... > '); if isempty(er2); er2 = 1; elseif er2 < 1; er2 = 1; end % check if dielectric is physical % prompt the user for the region side = input('Enter the side of the interface where the electric field is known (given)... > '); % if user entered something other than "r" "c" or "s" set default as "r" if isempty(side); side = 1; elseif side > 2; side = 2; end % check if dielectric is physical if side == 1; % prompt the user for the field E1 = input('Enter the electric field in side 1 in the form [Ex Ey Ez]... >'); E1n = E1(3)*[0 0 1]; % normal direction is +z E2n = E1n*er1/er2; % e-field boundary condition for normal component E1t = E1 - E1n; % tangential component of E1 E2t = E1t; % e-field boundary condition for tangential component E2 = E2t + E2n; elseif side == 2; % prompt the user for the field E2 = input('Enter the electric field in side 2 in the form [Ex Ey Ez]... >'); E2n = E2(3)*[0 0 1]; % normal direction is +z
- 4. E1n = E2n*er2/er1; % e-field boundary condition for normal component E2t = E2 - E2n; % tangential component of E2 E1t = E2t; % e-field boundary condition for tangential component E1 = E1t + E1n; else disp('Invalid specification, please re-try '); end % Display results disp(sprintf('The electric fields are E1 = (%d, %d, %d) V/m E2 = (%d, %d, %d) V/m',... E1(1), E1(2), E1(3), E2(1), E2(2), E2(3)))