Plot the potential surface and electric field strength vectors in the Oxy plane

Write Matlab program to:

1) Enter an expression , for example, lg (x) + y

2) Limit the space of the Oxy plane with xmax = ymax = 10

3) Use symbolic operations to compute and compute Ex and Ey components at all points in given space.

4) Plot the potential surface V and electric field vectors .

Answer 1

[Shishir Reddy]

Hi Nguyen

As per my understanding, you would like to write a MATLAB program that computes and visualizes the potential surface and electric field vectors from a user-defined mathematical expression over a specified 2D space.

Kindly refer the following snippets to achieve the tasks you've outlined (Assumption - ‘V’, ‘xmax’,’ ymax’ are defined)–

Computing the Electric field components –

Ex = -diff(V, x);
Ey = -diff(V, y);

Creating a grid for plotting –

[xGrid, yGrid] = meshgrid(linspace(-xmax, xmax, 20), linspace(-ymax, ymax, 20));

Evaluating the potential and electric field components on the grid

VGrid = double(subs(V, {x, y}, {xGrid, yGrid}));
ExGrid = double(subs(Ex, {x, y}, {xGrid, yGrid}));
EyGrid = double(subs(Ey, {x, y}, {xGrid, yGrid}));

Plotting the potential surface –

surf(xGrid, yGrid, VGrid);

Plotting the electric field vectors –

quiver(xGrid, yGrid, ExGrid, EyGrid);

For more information regarding the ‘diff’, ‘meshgrid’, ‘subs’, ‘surf’, ‘quiver’ functions, kindly refer to the following documentations -

https://www.mathworks.com/help/symbolic/sym.diff.html

https://www.mathworks.com/help/matlab/ref/meshgrid.html

https://www.mathworks.com/help/symbolic/sym.subs.html

https://www.mathworks.com/help/matlab/ref/surf.html

https://www.mathworks.com/help/matlab/ref/quiver.html

I hope this helps.

[Nguyen Duc]

Thank you so much, I really appreciate for your information!

[Nguyen Duc]

% Define constants

k = 8.99e9;% Coulomb's constant in N*m^2/C^2

q = 1e-9;% Charge in Coulombs

% Define grid for the Oxy plane

x = linspace(-1, 1, 50); % X-axis range

y = linspace(-1, 1, 50); % Y-axis range[X, Y] = meshgrid(x,y);

% Calculate the potential V at each point (X,Y)

% For a point charge at the origin:

r = sqrt(X.^2 + Y.^2); % Distance from the origin

V=k* q ./ r; % Potential (Avoid r = e to prevent infinity)

V(r == 0 ) NaN; % Set NaN at r = e to avoid infinity in plot

% Calculate the electric field component Ex and Ey

[Ex, Ey] = gradient(-V,x,y);

% Plot the potential surface

figure;

surf(X， Y， V，'EdgeColor'，'none');

colorbar;

title('Electric Potential Surface');

xlabel('x(m)");

ylabel("y(m)');

zlabel('Potential(V)');

view(3);% 3D view

% Overlay electric field vectors hold on; quiver(X, Y,Ex, Ey, 'k'); % Electric field vectors in black

hold off;

% Add labels for electric field plot title('Electric Potential Surface and el.V ric Field vectors');

xlabel('x(m)');

ylabel("y(m)');

zlabel('Potential (V)");

view(3); % Adjust viewing angle for better visualization

Do you think my code is ok? If it is not hope you can give me more helps to improve it. Thanks a lot!