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Is current density a vector or a scalar ...

Is current density a vector or a 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) increases in potential gradient ? (b) increase in temperature? ( c) increase in length? (d) increase in area of cross-section? (Assume that the other factors remain constant in each case).

Text Solution

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Current density is a vector quantity. Its direction is same as that of motion of positive charge.
Current, `I= n A e v_(d) `and `v_(d)= (eE)/(m) tau`
Current densitt, `J=I/A= n e V_(d) = "ne" xx eE/m tau`
`= "ne"^(2)tau/m (V/l)`
(a) With increase in potential gradient `(V//l)`, J increase. (b) With increase in temperature, `tau` decreases, so J decreases. ( C) With increase in length J decrases. (d) With increase in area, J remains unchanged as J is independent of A.
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