Error Using Gradient Function

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Carl
Carl 2011-10-6
I am attempting to write a program that will solve for the electric field and charge density (rho_v) at a point P given a function for voltage. This is a very straight forward problem on paper but I'm having some issues translating this to code. E is found with E = -(del)V and rho_v found with Gauss' Law. To start I shift the coordinates given for P from Cartesian to spherical since I find it makes Gauss' Law easier later. I believe I am using the gradient function correctly as it is described on the mathworks description page. But every time I run the program I get the following error:
Error in ==> gradient at 49
[msg,f,ndim,loc,rflag] = parse_inputs(f,varargin);
??? Output argument "varargout{2}" (and maybe others) not assigned during call to "C:\Program
Files\MATLAB\R2011a Student\toolbox\matlab\datafun\gradient.m>gradient".
Error in ==> Test at 19
[V_r,V_theta,V_phi] = gradient(V);
CODE
x = -3;
y = 1;
z = 2;
eta_0 = 8.85*10^-12;
r = sqrt(x^2 + y^2 + z^2);
theta = atan(sqrt(x^2 + y^2)/z);
phi = atan(y/x);
x = r*cos(theta);
y = r*sin(theta)*cos(phi);
z = r*cos(theta);
V = 5*x.^3*y.^2*z;
[V_r,V_theta,V_phi] = gradient(V);
E = [V_r,V_theta,V_phi];
rho_i = @(r,theta,phi)r.^2*sin(theta);
rho_f = triplequad(rho_i,0,r,0,pi,0,2*pi);
rho_v = (eta_0*E)/rho_f;
Any assistance solving this error would be greatly appreciated.

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回答（1 个）

Jan
Jan 2011-10-6
You "believe" that you are running gradient correctly, but did you check this? If you use the debugger either by setting a breakpoint or by dbtop if error you can find out very fast, that V is scalar, to be exact with the value 720. And you cannot calculate a gradient with 3 dimensions from a scalar.
Do you want the partial derivatives of "5*x.^3*y.^2*z"? This can be computed manually.

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