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? - Zigya
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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,   I = qt
                      = neAlt
Therefore,
Current per unit area i.e., current density 
               J =IA = nevd   
                                      lt = νd drift speed
               J =neeVml.τ 

              J = ne2m. l 

where m is mass of an electron and τ is the relaxation time. 

(a) current density increases with increase in potential gradient Vl.

(b) when temperature increases, relaxation time (τ) decreases and current density decreases. 

(c) when area of cross-section increases the current density J = IA decreases.

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