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Main Question or Discussion Point
This is driving me crazy. The derivation of the current distribution in a long cylindrical wire is extremely straightforward, giving
[tex]J(r) = J(a) \frac{J_0(k r)}{J_0(k a)}[/tex]
where [itex]J[/itex] is the current density, [itex]a[/itex] is the radius of the wire, and [itex]k[/itex] is the complex wave vector, which in a metal (with nearly no permittivity) is given by
[tex]k^2 \approx i \omega \mu \sigma[/tex]
[itex]J_0[/itex] is the Bessel function of order zero. These expressions match several books I've checked. But when I try to plot the current distribution for, say, copper in Matlab, it doesn't look like the plot in my book. The code is
The plot is attached. Is this correct? It doesn't seem to match the Wikipedia plot either. Does the current actually dip negative? It is otherwise qualitatively right, in that all of the current is concentrated near the edge, but I thought the max was at the very edge. What am I missing here?
Thanks
[tex]J(r) = J(a) \frac{J_0(k r)}{J_0(k a)}[/tex]
where [itex]J[/itex] is the current density, [itex]a[/itex] is the radius of the wire, and [itex]k[/itex] is the complex wave vector, which in a metal (with nearly no permittivity) is given by
[tex]k^2 \approx i \omega \mu \sigma[/tex]
[itex]J_0[/itex] is the Bessel function of order zero. These expressions match several books I've checked. But when I try to plot the current distribution for, say, copper in Matlab, it doesn't look like the plot in my book. The code is
Code:
mu = 1.2566290e6;
sigma = 5.96e7;
omega = 2*pi*1e4; %10 kHz
a = .05;
k = sqrt(1i*omega*mu*sigma);
r=0:.0001:.01;
J = besselj(0,k*r)/besselj(0,k*a);
rej = real(J);
plot(r,rej)
Thanks
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