(a) Define ‘current density’. Is it a scalar or a vector ? An electric field $\vec{E}$ is maintained in a metallic conductor. If $n$ be the number of electrons (mass $m$, charge $-e$) per unit volume in the conductor and $\tau$ its relaxation time, show that the current density $\vec{j} = \alpha \vec{E}$, where $\alpha = \left$ \frac{ne^2}{m} \right$ \tau$. OR (b) What is a Wheatstone bridge ? Obtain the necessary conditions under which the Wheatstone bridge is balanced.