Question

Assertion (A) : The current density (J) at a point in a conducting wire is in the direction of electric field (E) at that point. Reason (R) : A conducting wire obeys Ohm's law.

The radius of a conducting wire AB uniformly decreases from its one end A to another end B. It is connected across a battery. How will (i) electric field, (ii) current density, and (iii) mobility of electrons change from end A to end B ? Justify your answer in each case.

(i) Explain how free electrons in a metal at constant temperature attain an average velocity under the action of an electric field. Hence obtain an expression for it. (ii) Consider two conducting wires A and B of the same diameter but made of different materials joined in series across a battery. The number density of electrons in A is 1.5 times that in B. Find the ratio of drift velocity of electrons in wire A to that in wire B.

Define 'current density'. Is it a scalar or a vector ? An electric field 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 τ its relaxation time, show that the current density j = α E, where α = (ne²/m)τ.