Step 1: Start from the microscopic form of Ohm's law.
Ohm's law in point form links current density \(\vec{J}\) to the electric field \(\vec{E}\) inside a conductor by \(\vec{J}=\sigma\vec{E}\). The constant of proportionality \(\sigma\) is exactly the specific conductivity.
Step 2: State the definition from this relation.
Rearranging, \(\sigma=\dfrac{J}{E}\), so specific conductivity is the current density set up per unit electric field applied across the material. Equivalently, it is the conductance of a piece of the material having unit length and unit cross-sectional area.
Step 3: Obtain the unit from \(\sigma=J/E\).
Current density \(J\) has unit ampere per square metre \((\text{A m}^{-2})\) and electric field \(E\) has unit volt per metre \((\text{V m}^{-1})\). Hence
\[ [\sigma]=\frac{\text{A m}^{-2}}{\text{V m}^{-1}}=\frac{\text{A}}{\text{V m}}=\Omega^{-1}\text{m}^{-1} \]
using \(\dfrac{\text{A}}{\text{V}}=\Omega^{-1}\) (siemens).
Result: Specific conductivity is the reciprocal of resistivity, with unit siemens per metre.
\[\boxed{\text{Unit}=\text{S m}^{-1}=\Omega^{-1}\text{m}^{-1}}\]