Let potential difference V is applied across a conductor of length l and hence an electric field E produced inside the conductor.
∴ E = V/l ……. (i)
Let n = number density of free electrons
A = cross-sectional area of conductor
e = electrons charge.
∴ Number of free electrons present in length l of conductor = nAl
Total charge contained in length l which can contribute in current,
q = (nAl)e ……. (i)
The time taken by free electron to cross the length l of conductor is
t = l/υd ……… (ii)
where, υd = drift speed of electron.
∴ Current through the conductor [from Eqs. (i) (ii)]
I = q/t
∴ = neυd ,i.e., J ∝ υd Thus, current density of conductor is proportional to drift speed.
