Question

Derive an expression for the current density in terms of the drift velocity of electrons.

Answer 1

from above three attachments
we get

J = i/A ..... ..... (1)

i= n×A×v×e ............(2)

putting (2) in (1)

we get

J = n×A×v×e/A
J= n×v×e .......... is the required equation.

where
J- current density
A- cross section area
i - current
n- number of free electron per unit volume
v - drift velocity
e- charge on electron

therefore,
the required equation is

$j = n \times e \times v$
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