$$\sigma\propto (1-\chi_\text{v})$$
This means that diamagnetic materials are very good conductors of electricity; which they are.
As an example, the absolute value of magnetic susceptibility of silver is more than copper. So silver should be a better conductor of electricity (than copper); which it is.
By symmetry
$$\varsigma \propto (1-\chi_e),$$
where \(\varsigma\) is magnetic conductivity.
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