Question

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.

A potential difference V is applied across a conductor of length l and cross-sectional area A. Briefly explain how the current density j in the conductor will be affected if

Two conductors, made of the same material have equal lengths but different cross-sectional areas A₁ and A₂ (A₁ > A₂). They are connected in parallel across a cell. Show that the drift velocities of electrons in two conductors are equal.

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.