电磁基于Matlab实现理想圆柱形电流片的精确磁场.zip

Magnetic Field Of A Cylindrical Current Sheet

Calculates and displays the exact magnetic field of an ideal cylindrical current sheet making use of MATLAB

elliptic integral functions.

Author: D. Carlsmith

Table of Contents

Introduction...............................................................................................................................................................1

Set physical parameter values..................................................................................................................................1

Try this: Change the length and radius to observe the effect of aspect ratio........................................................1

Calculate ideal field of an infinitely long cylinder as a reference field strength.........................................................2

Try this: To profile the field along a different radial line, change the value of zline.............................................. 3

Try this: To profile the field along a line parallel to the axis at a different radius, pick a different target radial

value..................................................................................................................................................................... 4

Compare the axial line field to the exact axial field of an ideal coil...........................................................................5

Visualize magnetic field lines. ..................................................................................................................................6

Try this: Change the density of field lines ............................................................................................................ 6

References............................................................................................................................................................... 7

Introduction

The magnetic field of a cylindrical sheet of current provides a representation of the external field of a cylinder

uniformly magnetized along its symmetry axis and an approximation to a helically wound solenoid and is

Set physical parameter values

totalevaluationtime=tic;

mu0val=4*pi*1e-7; % permeability of the vacuum set to unity

Ival=1; % total current in the cymindrical sheet

Try this: Change the length and radius to observe the effect of aspect ratio.

Lval=5; % total length of the cylinder

Rval=1; % radius of the cylinder

M=Ival/Lval; % equivalent magnetization

1

vars=[mu0 I L R];

The cylinder is assumed to be centered on the origin. The symbol names are essentially those in Ref [1].

xi_p = z+L/2;

xi_m = z-L/2;

alpha_p=1./sqrt(xi_p.^2+(rho+R).^2);

alpha_m=1./sqrt(xi_m.^2+(rho+R).^2);

beta_p=xi_p.*alpha_p;

beta_m=xi_m.*alpha_m;

g=(rho-R)./(rho+R);

k2_p=(xi_p.^2+(rho-R).^2)./(xi_p.^2+(rho+R).^2);

k2_m=(xi_m.^2+(rho-R).^2)./(xi_m.^2+(rho+R).^2);

P_2=@(k,g)( (1./(g.^2-1)).*(...

g.*(Pi(k,g)-K(k))+g.^2*Pi(k,g)-K(k)) );

B_r=(mu0*M*R./pi)*(alpha_p.*P_1(k_p,g) -alpha_m.*P_1(k_m,g));

B_z=(mu0*M*R./(pi.*(rho+R))).*(beta_p.*P_2(k_p,g)-beta_m.*P_2(k_m,g));

Substitute values for parameters and convert these formulae to MATLAB

functions of coordinates.

B_rF=matlabFunction(subs(B_r,vars,vals));

B_zF=matlabFunction(subs(B_z,vars,vals));

Calculate magnetic field components over a grid in r and z z.

L=vals(3);

2

nr=20; %number or radial values

nz=40; %number of axial values

for rt=.0001:rmax/nr:rmax %nr values in radius spanning 0 to 4*radius

ir=ir+1;

iz=0;

for zt=-zmax:2*zmax/nz:zmax %nz values of z spanning twice the length

iz=iz+1;

Brtest(ir,iz)=B_rF(rt,zt);

Bztest(ir,iz)=B_zF(rt,zt);

rtest(ir,iz)=rt;

tocfieldevaltime =

68.048

timeperevaluation=tocfieldevaltime/prod(size(Brtest))

timeperevaluation =

0.082986

The calculation of the field over a grid takes some time. After it is complete, exercise this section of the script to

profile the field.

Plot the radial and azimuth field components along a central radial line and

along a line almost on the symmetry axis.

figure

[minValuez,closestIndexz] = min(abs(ztest(1,:)-zline));

indz=closestIndexz;zline=ztest(1,closestIndexz);

maxBz=max(Bztest(:,indz));

maxBr=max(Brtest(:,indz));

maxB=max(maxBz,maxBr);

minBz=min(Bztest(:,indz));

3