Question

MATLAB CODE:

The electric potential around a charged particle is given by , where ε=8.854x10-12?=14????C/Nm2 , q is the charge and r is the distance from the particle. The electric potential of 2 particles at a point P is given by , where q1 and q2 are the particles charges and r1 and r2?=14??(?1?1+?2?2)are distances from the particles to P. Two particles with charges q1=2x10-10 C and q2=3x10-10 C are located in the x-y plane at (0.25,0) and (-.25,0). Calculate and plot the electric potential due to the particles at points in the x-y plane located in the domain -0.3<=x<=0.3 and -0.3<=y<=0.3.

Thank you :)

Answer 1

       This simple program computes the Electric Fields due to dipole  
%           in a 2-D plane using the Coulomb's Law
%-------------------------------------------------------------------------%
clc
close all; clear all;
%-------------------------------------------------------------------------%
%                   SYMBOLS USED IN THIS CODE                             
%-------------------------------------------------------------------------%
% E = Total electric field
% Ex = X-Component of Electric-Field
% Ey = Y-Component of Electric-Field
% n = Number of charges
% Q = All the 'n' charges are stored here
% Nx = Number of grid points in X- direction
% Ny = Number of grid points in Y-Direction
% eps_r = Relative permittivity
% r = distance between a selected point and the location of charge
% ex = unit vector for x-component electric field
% ey = unit vector for y-component electric field
%-------------------------------------------------------------------------%
%-------------------------------------------------------------------------%
%                         INITIALIZATION                                  
%          Here, all the grid, size, charges, etc. are defined
%-------------------------------------------------------------------------%
% Constant 1/(4*pi*epsilon_0) = 9*10^9
k = 9*10^9;
% Enter the Relative permittivity
eps_r = 1;
charge_order = 10^-9; % milli, micro, nano etc..
const = k*charge_order/eps_r;
% Enter the dimensions
Nx = 101; % For 1 meter
Ny = 101; % For 1 meter
% Enter the number of charges.
n = 2;
% Electric fields Initialization
E_f = zeros(Nx,Ny);
Ex = E_f;
Ey = E_f;
% Vectors initialization
ex = E_f;
ey = E_f;
r = E_f;
r_square = E_f;
% Array of charges
Q = [1,-1];
% Array of locations
X = [5,-5];
Y = [0,0];
%-------------------------------------------------------------------------%
%                   COMPUTATION OF ELECTRIC FIELDS
%-------------------------------------------------------------------------%
%  Repeat for all the 'n' charges
for k = 1:n
    q = Q(k);
    
    % Compute the unit vectors
    for i=1:Nx
        for j=1:Ny
            r_square(i,j) = (i-51-X(k))^2+(j-51-Y(k))^2;
            r(i,j) = sqrt(r_square(i,j));
            ex(i,j) = ex(i,j)+(i-51-X(k))./r(i,j);
            ey(i,j) = ey(i,j)+(j-51-Y(k))./r(i,j);
        end
    end
    
    
    E_f = E_f + q.*const./r_square;
    Ex = Ex + E_f.*ex.*const;
    Ey = Ex + E_f.*ey.*const;
end
%-------------------------------------------------------------------------%
%                   PLOT THE RESULTS
%-------------------------------------------------------------------------%
x_range = (1:Nx)-51;
y_range = (1:Ny)-51;
contour_range = -8:0.02:8;
contour(x_range,y_range,E_f',contour_range,'linewidth',0.7);
axis([-15 15 -15 15]);
colorbar('location','eastoutside','fontsize',12);
xlabel('x ','fontsize',14);
ylabel('y ','fontsize',14);
title('Electric field distribution, E (x,y) in V/m','fontsize',14);
%-------------------------------------------------------------------------%
%                  REFERENCE
% SADIKU, ELEMENTS OF ELECTROMAGNETICS, 4TH EDITION, OXFORD
%-------------------------------------------------------------------------%