我的代码没有为垂直于电荷环的平面正确地绘制正确的轮廓图。 我的问题是等高线图无法填充2D空间。
我制作了两个版本的代码，一个使用for循环来计算 Riemann sum和另一个仅使用sum命令。两者都依靠 'subs'命令，用于将网格中的值替换为我的表达式中的V（电势）。
版本1（用于循环）：
%% Computing a symbolic expression for V for anywhere in space
syms x y z % phiprime is angle that an elemental dq of the circular
charge is located at, x,y and z are arbitrary points in space outside the
charge distribution
N = 200; % number of increments to sum
R = 2; % radius of circle is 2 meters
dphi = 2*pi/N; % discretizing the circular line of charge which spans 2pi
integrand = 0;
for phiprime = 0:dphi:2*pi
% phiprime ranges from 0 to 2pi in increments of dphi
integrand = integrand + dphi./(sqrt(((x - R.*cos(phiprime) )).^2 + ((y -
R.*sin(phiprime) ).^2) + z.^2));
end
intgrl = sum(integrand);
% uncessary but harmless step that I leave to show that I am using the
sum of the above expression for each dphi
eps0 = 8.854e-12;
kC = 1/(4*pi*eps0);
rhol = 1*10^-9; % linear charge density
Vtot = kC*rhol*R.*intgrl; % symbolic expression for Vtot
%% Graphing V & E in plane perpedicular to ring & passing through center
[Y1, Z1] = meshgrid(-4:.5:4, -4:.5:4);
Vcont1 = subs(Vtot, [x,y,z], {0,Y1,Z1}); % Vcont1 stands for V contour; 1
is because I do the plane of the ring next
contour(Y1,Z1,Vcont1)
xlabel('y - axis [m]')
ylabel('z - axis [m]')
title('V in a plane perpendicular to a ring of charge (N = 200)')
str = {'Red line is side view', 'of ring of charge'};
text(-1,2,str)
hold on
% visually displaying line of charge on plot
circle = rectangle('Position',[-2 0 4 .1],'Curvature',[1,1]);
set(circle,'FaceColor',[1, 0, 0],'EdgeColor',[1, 0, 0]);
% taking negative gradient of V and finding symbolic equations for Ex, Ey
and Ez
g = gradient(-1.*(kC*rhol*R.*intgrl),[x,y,z]);
%% now substituting all the values of the 2D coordinate system for the
symbolic x and y variables to get numeric values for Ex and Ey
Ey1 = subs(g(2), [x y z], {0,Y1,Z1});
Ez1 = subs(g(3), [x y z], {0,Y1,Z1});
E1 = sqrt(Ey1.^2 + Ez1.^2); % full numeric magnitude of E in y-z plane
Eynorm1 = Ey1./E1; % This normalizes the electric field lines
Eznorm1 = Ez1./E1;
quiver(Y1,Z1,Eynorm1,Eznorm1);
hold off
版本2（使用sum命令）：
syms x y z
R = 2; % radius of circle is 2 meters
N=100;
dphi = 2*pi/N; % discretizing the circular line of charge which spans 2pi
phiprime = 0:dphi:2*pi; %phiprime ranges from 0 to 2pi in increments of
dphi
integrand = dphi./(sqrt(((x - R.*cos(phiprime) )).^2 + ((y -
R.*sin(phiprime) ).^2) + z.^2));
phiprime = 0:dphi:2*pi;
intgrl = sum(integrand); % Reimann sum performed here
eps0 = 8.854e-12;
kC = 1/(4*pi*eps0);
rhol = 1*10^-9; % linear charge density
Vtot = kC*rhol*R.*intgrl; % symbolic expression for Vtot
此后，版本2的所有其他内容都与版本1相同（用符号x，y，z等代替）
我会发布代码产生的图像，但是显然您需要10声望。谢谢stackoverflow。如果没有这些图片，这将更加令人困惑。
我的代码产生的矢量场是正确的，而轮廓图似乎只在圆环的两端使用了几个点，并将它们与奇怪的菱形形状的直线相连。我无法填补它。
我没有收到任何错误消息。轮廓线以奇怪的菱形形状围绕环的末端（势能接近无穷大）积累，但未在其他任何地方绘制。我需要等高线图来填充2D网格
答案 0 :(得分：0)
我从MATLAB社区收到了有关此问题的解决方案，并在此处发布了有关该问题的信息：
我会在这里发布，但是这种“您无法发布图像，因为您的信誉不高”会使我的解释过于抽象和难以理解，因此请查看一下您是否遇到了MATLAB等高线图问题，并且想看看我的问题和解决方法