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%% 3D电偶极子电场线可视化（连续版） clear; clc; close all; % 常数设置 eps0 = 8.854e-12; % 真空介电常数 q = 1e-9; % 电荷量 (C) d = 0.2; % 偶极子间距 (m) k = 1/(4pieps0); % 常数系数 % 创建更高分辨率的3D计算网格 (从25提高到50) [x, y, z] = meshgrid(linspace(-0.6, 0.6, 50)); % 预分配电场分量数组 Ex = zeros(size(x)); Ey = zeros(size(y)); Ez = zeros(size(z)); % 计算3D电场分量 for i = 1:numel(x) r = [x(i), y(i), z(i)]; % 正电荷位置 (0,0,d/2) r1 = r - [0, 0, d/2]; r1_norm = norm(r1); E1 = k * q * r1 / (r1_norm^3 + eps); % 负电荷位置 (0,0,-d/2) r2 = r - [0, 0, -d/2]; r2_norm = norm(r2); E2 = -k * q * r2 / (r2_norm^3 + eps); E_total = E1 + E2; Ex(i) = E_total(1); Ey(i) = E_total(2); Ez(i) = E_total(3); end % 计算电场强度 E_magnitude = sqrt(Ex.^2 + Ey.^2 + Ez.^2); %% 3D电场线可视化（更连续） fig1 = figure('Position', [100, 100, 1200, 900], 'Name', '3D电偶极子电场线', 'Color', 'w'); ax1 = axes(fig1); hold(ax1, 'on'); % 设置更多流线起始点（提高theta和phi的分辨率） theta = linspace(0, 2pi, 32); % 从16提高到32 phi = linspace(0, pi, 16); % 从8提高到16 [sx, sy, sz] = spherePoints(0.05, theta, phi); sx = sx(:); sy = sy(:); sz = sz(:) + d/2; % 绘制更连续的电场线（调整步长和最大点数） verts = stream3(x, y, z, Ex, Ey, Ez, sx, sy, sz, [0.01, 10000]); % 减小步长，增加最大点数 streamline(verts); % 添加颜色映射（根据电场强度） hLines = streamline(verts); E_values = interp3(x, y, z, E_magnitude, verts{1}(:,1), verts{1}(:,2), verts{1}(:,3)); set(hLines, 'LineWidth', 2, 'Color', [0.8 0.2 0.2]); colormap(ax1, jet); colorbar(ax1); title(ax1, '电场强度 (V/m)'); caxis(ax1, [min(E_values) max(E_values)]); % 绘制电荷 pos_charge = [0, 0, d/2]; neg_charge = [0, 0, -d/2]; scatter3(ax1, pos_charge(1), pos_charge(2), pos_charge(3), 200, 'r', 'filled'); scatter3(ax1, neg_charge(1), neg_charge(2), neg_charge(3), 200, 'b', 'filled'); % 添加标题和标签 title(ax1, '电偶极子电场线 (连续版)', 'FontSize', 16, 'FontWeight', 'bold'); xlabel(ax1, 'x (m)', 'FontSize', 12); ylabel(ax1, 'y (m)', 'FontSize', 12); zlabel(ax1, 'z (m)', 'FontSize', 12); grid(ax1, 'on'); axis(ax1, 'equal'); view(ax1, 45, 30); % 添加图例 legend(ax1, {'电场线', '正电荷 (+q)', '负电荷 (-q)'}, 'Location', 'northeast'); hold(ax1, 'off'); %% 3D磁偶极子磁场线可视化（连续版） clear x y z Ex Ey Ez; % 清除电场变量 % 常数设置 mu0 = 4pi1e-7; % 真空磁导率 m0 = 1; % 磁矩大小 (A·m²) % 创建更高分辨率的3D计算网格 [x, y, z] = meshgrid(linspace(-0.6, 0.6, 50)); % 预分配磁场分量数组 Hx = zeros(size(x)); Hy = zeros(size(y)); Hz = zeros(size(z)); % 计算3D磁场分量 for i = 1:numel(x) r = [x(i), y(i), z(i)]; r_norm = norm(r) + eps; r_hat = r / r_norm; m = [0, 0, m0]; % z方向磁矩 % 磁偶极子磁场公式 (闭合回路) H = (mu0/(4pi)) * (3dot(m, r_hat)r_hat - m) / r_norm^3; Hx(i) = H(1); Hy(i) = H(2); Hz(i) = H(3); end % 计算磁场强度 H_magnitude = sqrt(Hx.^2 + Hy.^2 + Hz.^2); %% 3D电场线可视化 fig1 = figure('Position', [100, 100, 1200, 900], 'Name', '3D电偶极子电场线', 'Color', 'w'); ax1 = axes(fig1); hold(ax1, 'on'); % 设置流线起始点 theta = linspace(0, 2pi, 16); phi = linspace(0, pi, 8); [sx, sy, sz] = spherePoints(0.05, theta, phi); sx = sx(:); sy = sy(:); sz = sz(:) + d/2; % 绘制电场线并保存句柄 h_stream = streamline(stream3(x, y, z, Ex, Ey, Ez, sx, sy, sz)); set(h_stream, 'LineWidth', 1.5, 'Color', [0.8 0.2 0.2]); % 绘制电荷并保存句柄 h_pos = scatter3(ax1, pos_charge(1), pos_charge(2), pos_charge(3), 200, 'r', 'filled'); h_neg = scatter3(ax1, neg_charge(1), neg_charge(2), neg_charge(3), 200, 'b', 'filled'); % 添加标题和标签 title(ax1, '电偶极子电场线 (从正电荷到负电荷)', 'FontSize', 16, 'FontWeight', 'bold'); xlabel(ax1, 'x (m)', 'FontSize', 12); ylabel(ax1, 'y (m)', 'FontSize', 12); zlabel(ax1, 'z (m)', 'FontSize', 12); grid(ax1, 'on'); axis(ax1, 'equal'); view(ax1, 45, 30); % 正确设置图例 - 使用保存的句柄 legend(ax1, [h_stream(1), h_pos, h_neg], {'电场线', '正电荷 (+q)', '负电荷 (-q)'}, 'Location', 'northeast'); hold(ax1, 'off'); %% 3D磁场线可视化（更连续） fig2 = figure('Position', [100, 100, 1200, 900], 'Name', '3D磁偶极子磁场线', 'Color', 'w'); ax2 = axes(fig2); hold(ax2, 'on'); % 设置更多流线起始点 theta = linspace(0, 2pi, 48); % 从24提高到48 r = 0.15; sx = r * cos(theta); sy = r * sin(theta); sz = zeros(size(sx)); % 在更多平面添加起始点（从3层增加到5层） sx = [sx, sx0.7, sx0.85, sx1.15, sx1.3]; sy = [sy, sy0.7, sy0.85, sy1.15, sy1.3]; sz = [sz, sz+0.08, sz+0.15, sz-0.08, sz-0.15]; % 绘制更连续的磁场线 verts = stream3(x, y, z, Hx, Hy, Hz, sx, sy, sz, [0.005, 20000]); % 更小步长，更多点数 hLines = streamline(verts); % 添加颜色映射（根据磁场强度） H_values = interp3(x, y, z, H_magnitude, verts{1}(:,1), verts{1}(:,2), verts{1}(:,3)); set(hLines, 'LineWidth', 2, 'Color', [0.2 0.4 0.8]); colormap(ax2, jet); colorbar(ax2); title(ax2, '磁场强度 (A/m)'); caxis(ax2, [min(H_values) max(H_values)]); % 绘制磁偶极子（更精细的小环形电流） plotCurrentLoop(ax2, 0, 0, 0, 0.05); % 添加标题和标签 title(ax2, '磁偶极子磁场线 (连续版)', 'FontSize', 16, 'FontWeight', 'bold'); xlabel(ax2, 'x (m)', 'FontSize', 12); ylabel(ax2, 'y (m)', 'FontSize', 12); zlabel(ax2, 'z (m)', 'FontSize', 12); grid(ax2, 'on'); axis(ax2, 'equal'); view(ax2, 45, 30); % 添加图例 legend(ax2, {'磁场线', '磁偶极子 (环形电流)'}, 'Location', 'northeast'); hold(ax2, 'off'); %% 辅助函数 function [sx, sy, sz] = spherePoints(radius, theta, phi) % 在球面上生成点 [THETA, PHI] = meshgrid(theta, phi); sx = radius * sin(PHI) .* cos(THETA); sy = radius * sin(PHI) .* sin(THETA); sz = radius * cos(PHI); end function plotCurrentLoop(ax, cx, cy, cz, radius) % 绘制更精细的环形电流（增加点数） theta = linspace(0, 2pi, 100); % 从50提高到100 x = radius cos(theta) + cx; y = radius * sin(theta) + cy; z = zeros(size(theta)) + cz; % 绘制环（更平滑） plot3(ax, x, y, z, 'k', 'LineWidth', 3); % 添加电流方向箭头（更多箭头） arrowTheta = linspace(0, 2pi, 12); % 从4增加到12个箭头 for i = 1:length(arrowTheta) angle = arrowTheta(i); axPos = [radiuscos(angle), radiussin(angle), 0]; axDir = [-sin(angle), cos(angle), 0]; quiver3(ax, axPos(1), axPos(2), axPos(3), ... axDir(1)0.1, axDir(2)0.1, axDir(3), ... 0.5, 'k', 'LineWidth', 2, 'MaxHeadSize', 1); end % 添加中心点 scatter3(ax, cx, cy, cz, 100, 'k', 'filled'); end %% 3D磁场线可视化 fig2 = figure('Position', [100, 100, 1200, 900], 'Name', '3D磁偶极子磁场线', 'Color', 'w'); ax2 = axes(fig2); hold(ax2, 'on'); % 设置流线起始点 theta = linspace(0, 2pi, 24); r = 0.15; sx = r * cos(theta); sy = r * sin(theta); sz = zeros(size(sx)); sx = [sx, sx0.8, sx1.2]; sy = [sy, sy0.8, sy1.2]; sz = [sz, sz+0.1, sz-0.1]; % 绘制磁场线并保存句柄 h_mag_stream = streamline(stream3(x, y, z, Hx, Hy, Hz, sx, sy, sz)); set(h_mag_stream, 'LineWidth', 1.5, 'Color', [0.2 0.4 0.8]); % 绘制磁偶极子并保存句柄 h_loop = plotCurrentLoop(ax2, 0, 0, 0, 0.05); % 添加标题和标签 title(ax2, '磁偶极子磁场线 (闭合回路)', 'FontSize', 16, 'FontWeight', 'bold'); xlabel(ax2, 'x (m)', 'FontSize', 12); ylabel(ax2, 'y (m)', 'FontSize', 12); zlabel(ax2, 'z (m)', 'FontSize', 12); grid(ax2, 'on'); axis(ax2, 'equal'); view(ax2, 45, 30); % 正确设置图例 - 使用保存的句柄 legend(ax2, [h_mag_stream(1), h_loop], {'磁场线', '磁偶极子 (环形电流)'}, 'Location', 'northeast'); hold(ax2, 'off'); %% 辅助函数 % ...（保持不变）... function h_loop = plotCurrentLoop(ax, cx, cy, cz, radius) % 重写函数以返回绘图句柄 % 绘制环形电流 theta = linspace(0, 2pi, 50); x = radius cos(theta) + cx; y = radius * sin(theta) + cy; z = zeros(size(theta)) + cz; % 绘制环并保存句柄 h_loop = plot3(ax, x, y, z, 'k', 'LineWidth', 3); % 添加电流方向箭头 arrowTheta = [0, pi/2, pi, 3pi/2]; for i = 1:length(arrowTheta) angle = arrowTheta(i); axPos = [radiuscos(angle), radiussin(angle), 0]; axDir = [-sin(angle), cos(angle), 0]; quiver3(ax, axPos(1), axPos(2), axPos(3), ... axDir(1)0.1, axDir(2)*0.1, axDir(3), ... 0.5, 'k', 'LineWidth', 2, 'MaxHeadSize', 1); end % 添加中心点 scatter3(ax, cx, cy, cz, 100, 'k', 'filled'); end错误: 文件: untitled.m 行: 268 列: 19 函数 'plotCurrentLoop' 已在此作用域内声明。报错了

<think>我们注意到错误信息：“函数'plotCurrentLoop'已在此作用域内声明。”这是......

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