Matlab如何精确计算理想圆柱电流片产生的电磁场？

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1+内容介绍：圆柱形电流片产生的磁场代表了沿其对称轴均匀磁化的圆柱体的外部场，并近似于螺旋卷绕的螺线管。

1 内容介绍

The magnetic field of a cylindrical sheet of current provides a representation of the external field of a cylinderuniformly magnetized along its symmetry axis and an approximation to a helically wound solenoid and isexpressible in terms of elliptical integral functions.

2 部分代码

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);

k_p=sqrt(k2_p);

k_m=sqrt(k2_m);

K=@(k)ellipticK((1-k.^2));

E=@(k)ellipticE((1-k.^2));

Pi=@(k,g)ellipticPi(1-g.^2,(1-k.^2));

P_1=@(k,g)(K(k)-(2./(1-k.^2)).*(K(k)-E(k)));

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));

3 运行结果

4 参考文献

References

[1] Alessio Caciagli, Roel J. Baars, Albert P. Philipse, Bonny W.M. Kuipers, ''Exact expression for the magneticfield of a finite cylinder with arbitrary uniform magnetization,'' Journal of Magnetism and Magnetic Materials,

Volume 456, 2018, Pages 423-432, ISSN 0304-8853,.

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