Is current density a vector quantity or scalar quantity? Deduce the relation between current density and potential difference across a current carrying conductor of length l, area of cross-section A and number density of free electrons n. How does the current density in a conductor vary with
(a) increase in potential gradient,
(b) increase in temperature,
(c) increase in area of cross-section?

Current-density is a vector quantity.
If potential difference V is applied across a conductor of length 'l' and area of cross-section 'A' having number of free electrons per unit volume n.
Then, the charge in the conductor
and current,
Therefore,
Current per unit area i.e., current density
where m is mass of an electron and is the relaxation time.
(a) current density increases with increase in potential gradient .
(b) when temperature increases, relaxation time (τ) decreases and current density decreases.
(c) when area of cross-section increases the current density decreases.
821 Views