(a) Define the term 'conductivity' of a metallic wire. Write its SI unit.
(b) Using the concept of free electrons in a conductor, derive the expression for the conductivity of a wire in te'rms of number density and relaxation time. Hence obtain the relation between current density and the applied electric field E.

Explanation

### Solution:

**(a)** **Definition of Conductivity:**
Conductivity (\( \sigma \)) of a metallic wire is defined as the ability of the material to conduct electric current. It quantifies how easily electrons can flow through the material when an electric field is applied. Mathematically, conductivity is the reciprocal of resistivity (\( \rho \)).

**SI Unit of Conductivity:**
The SI unit of conductivity is Siemens per meter (S/m). This can also be expressed as ohm inverse meter inverse (\( \Omega^{-1} \cdot m^{-1} \)).

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