Please help me in this Physics Project

Hello everybody, I'm doing a physics project with Matlab. There are some problems and I hope you and everyone here can help me.

The project is:

Draw the electric field and the vector of electric field intensity.
The requirements are: 
• Initialize variables (e.g., potential V(x,y), graphics).
• Evaluate electric field as Ex
 = – dV/ x and Ey
 = – dV/ y.
• Loop over all grid points and evaluate V(x,y) and E(x,y) on grid.
• Compute potential at the grid point.
• Compute components of the electric field.
 • Normalize E-field vectors to unit length.
• Plot contours of constant electric potential.
• Add electric field direction to potential contour plot.

I have found a code for reference but I don't understand it and when I tested with Matlab, the code had a problem. Here's the code:

    if true
      % code
  % e_and_v - Compute electric field from potential
  % and graph potential contours and E-field direction
  clear all; help e_and_v; % Clear memory; print header
  %@ Initialize variables (e.g., potential V(x,y), graphics)
  fprintf('Enter potential V(x,y) as an equation \n');
  fprintf('For example: log(x^2 + y^2) \n');
  V = input(': ','s'); % Read in V(x,y) as text string
  NGrid = 20; % Number of grid points for plots
  xMax = 5; % Values plotted from x= -xMax to x= xMax
  yMax = xMax; % Values plotted from y= -yMax to y= yMax
  for i=1:NGrid
   xPlot(i) = -xMax + (i-1)/(NGrid-1)*(2*xMax); % x values to plot
   yPlot(i) = -yMax + (i-1)/(NGrid-1)*(2*yMax); % y values to plot
  end
  %@ Evaluate electric field as Ex = (-1)*dV/dx and Ey = (-1)*dV/dy
  % Note use of symop command to perform symbolic multiplication by -1
  Ex = symop( '-1', '*', diff(V,'x') );
  Ey = symop( '-1', '*', diff(V,'y') );
  fprintf('Electric field components are \n');
  disp(['x component : ', Ex]);
  disp(['y component : ', Ey]);
  %@ Loop over all grid points and evaluate V(x,y) and E(x,y) on grid
  for i=1:NGrid
   y = yPlot(i);
   for j=1:NGrid
   x = xPlot(j);
   %@ Compute potential at the grid point
   VPlot(i,j) = eval( V ); % Potential V(x,y)
   %@ Compute components of the electric field
   ExPlot(i,j) = eval( Ex );
   EyPlot(i,j) = eval( Ey );

   %@ Normalize E-field vectors to unit length
   MagnitudeE = sqrt( ExPlot(i,j)^2 + EyPlot(i,j)^2 );
   ExPlot(i,j) = ExPlot(i,j)/MagnitudeE;
   EyPlot(i,j) = EyPlot(i,j)/MagnitudeE;

   end
  end

    end

Here's the error:

??? Undefined function or method 'symop' for input arguments of
type 'sym'.

Error in ==> Untitled at 17

Ex = symop( '-1', '*', diff(V,'x') );

Can anyone explain the code and the error for me? For the code, I don't understand the thing:

    if true
      for i=1:NGrid
   xPlot(i) = -xMax + (i-1)/(NGrid-1)*(2*xMax); % x values to plot
   yPlot(i) = -yMax + (i-1)/(NGrid-1)*(2*yMax); % y values to plot
  end
  %@ Evaluate electric field as Ex = (-1)*dV/dx and Ey = (-1)*dV/dy
  % Note use of symop command to perform symbolic multiplication by -1
  Ex = symop( '-1', '*', diff(V,'x') );
  Ey = symop( '-1', '*', diff(V,'y') );
    end

and 

    if true
      for i=1:NGrid
   y = yPlot(i);
   for j=1:NGrid
   x = xPlot(j);
   %@ Compute potential at the grid point
   VPlot(i,j) = eval( V ); % Potential V(x,y)
   %@ Compute components of the electric field
   ExPlot(i,j) = eval( Ex );
   EyPlot(i,j) = eval( Ey );
    end

Thank you so much. Your help will be really appreciated.

Answer 1

[Youssef Khmou]

Hi Nghia,

some functions are missing in that code, instead i wrote a version that can be useful, try :

N=100; % numbef of points
l=linspace(0,1,N); % linear spacing
[x,y]=meshgrid(l); % a plate of length 1m as example
V=100*sin(x.*y); %  example of potential distriibution.
figure(1),
surf(x,y,V), title(' Potential distribution' );
[Ex,Ey]=gradient(V);
Ex=Ex*(-1);
Ey=Ey*(-1);
% Modulus 
E=sqrt(Ex^2+Ey^2);
E=E/norm(E); %  Normalization so that ||E(x,y)||=1.
figure(2),
contour(E);

 figure(3)
contour(x,y,V);
hold on,
quiver(x,y,Ex,Ey)

[Nghia]

Thank you. But your code is just for one case, right? How can I transfer it into general?

[Nghia]

I want the user can enter the function of V instead of using V=100*sin(x.*y). How ever when I write V= input(': ','s'), your code had errors.

PLEASE HELP ME!!! THANK YOU.

Answer 2

[Walter Roberson]

symop() is before MATLAB 7.0 (R14). See http://www.mathworks.com/matlabcentral/newsreader/view_thread/82603

[Walter Roberson]

Vfun = str2func( ['@(x, y) ', input(': ', 's') ] );
V = Vfun(x, y);

[Nghia]

Thank you so much, Walter :)

[Youssef Khmou]

that is efficient answer .