电磁场实验报告

实验一：静电场的分析与求解

1.求二维标量场u（r）=y^2-x的梯度

[x,y]=meshgrid(-2:.2:2,-2:.2:2);

z=y.^2-x;

[px,py]=gradient(z,.2,.2);

contour(z)

hold on

quiver(px,py)

hold off

title('等值线与梯度');

2.2个等量同号点电荷组成的点电荷系的电势分布图clear

v='1./((x-3).^2+y.^2).^0.5+1./((x+3).^2+y.^2).^0.5'; xmax=10;

ymax=10;

ngrid=30;

xplot=linspace(-xmax,xmax,ngrid);

[x,y]=meshgrid(xplot);

vplot=eval(v);

[explot,eyplot]=gradient(-vplot);

clf;

subplot(1,2,1),meshc(vplot);

xlabel('x');

ylabel('y');

zlabel('电位');

subplot(1,2,2),axis([-xmax xmax -ymax ymax]); cs=contour(x,y,vplot);

clabel(cs);

hold on

quiver(x,y,explot,eyplot)

xlabel('x');

ylabel('y');

hold off

3.电偶极子的场（等位线和梯度）

clear;

clf;

q=2e-6;

k=9e9;

a=1.5;

b=-1.5;

x=-6:0.6:6;

y=x;

[X,Y]=meshgrid(x,y);

rp=sqrt((X-a).^2+(Y-b).^2);

rm=sqrt((X+a).^2+(Y+b).^2);

V=q*k*(1./rp-1./rm);

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

AE=sqrt(Ex.^2+Ey.^2);

Ex=Ex./AE;

Ey=Ey./AE;

cv=linspace(min(min(V)),max(max(V)),49);

contourf(X,Y,V,cv,'k-')

title('电偶极子的场'),hold on

quiver(X,Y,Ex,Ey,0.7)

plot(a,b,'wo',a,b,'w+')

plot(-a,-b,'wo',-a,-b,'w-')

xlabel('x');ylabel('y');

hold off

实验二：磁感应强度求解

1.单匝环形通电线圈形成的磁感应强度

clear

rh=2.5;i0=10;mu0=4*pi*1e-7;n=11

m=(n+1)/2

xmax=6;ymax=6;ngrid=40;

cx(1:ngrid,1:ngrid)=zeros;cy(1:ngrid,1:ngrid)=zeros; c0=mu0/4*pi;

nh=20;

ngrid1=nh+1;

xmax1=0;

ymax1=2*pi;

xplot=linspace(-xmax,ymax,ngrid);

yplot=linspace(-xmax,ymax,ngrid);

theta0=linspace(0.2*pi,21);

theta1=theta0(1:nh);

y1=rh*cos(theta1);

z1=rh*sin(theta1);

theta2=theta0(2:nh+1);

y2=rh*cos(theta2);

z2=rh*sin(theta2);

dlx=0;dly=y2-y1;dlz=z2-z1;

xc=[-(n-1)/2:2:(n-1)/2];

yc=(y2+y1)/2;

zc=(z2+z1)/2;

for k=1:m

for i=1:ngrid

for j=1:ngrid

rx=xplot(j)-xc(k);

ry=yplot(i)-yc;

rz=0-zc;

r3=sqrt(rx.^2+ry.^2+rz.^2).^3;

dlxr_x=dly.*rz-dlz.*ry;

dlxr_y=dlz.*rx-dlx.*rz;

bx(i,j)=sum(c0*i0*dlxr_x./r3);

by(i,j)=sum(c0*i0*dlxr_y./r3);

end

end

cx(1:ngrid,1:ngrid)=cx(1:ngrid,1:ngrid)+bx(1:ngrid,1:ngrid);

cy(1:ngrid,1:ngrid)=cy(1:ngrid,1:ngrid)+by(1:ngrid,1:ngrid); end

quiver(xplot,yplot,cx,cy);

hold on

plot(xc,rh, 'r*')

hold on

plot(xc,-rh,'r*')

n =

11

m =

6