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Tesla23
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The wikipedia article states that this approximate impedance is calculated assuming a sinusoidal current distribution on a centre-fed dipole.

There are no fields in the conductors as this analysis assumes perfect conductors.

This formula is an approximation, and the term

\$Ci(\frac{2ka^2}{L}) \$

which goes as \$log(\frac{2ka^2}{L}) \$ as \$a \rightarrow 0\$

and will dominate the reactance as \$a \rightarrow 0\$ for all element lengths not \$ \lambda/2\$, and the fact that it doesn't have any affect at precisely \$ \lambda/2\$ I think should be seen as a limitation of the approximation.

Tesla23
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