A straight copper wire of length `l = 1000 m` and cross sectional area `S = 1.0 mm^(2)` carries a current `I = 4.5 A`. Assuming that one free electron corresponds to each copper atom, find,
(a) the time it takes an electron to displace from one end of the wire to the other,
(b) the sum of electric froces acting on all free electrons in the given wire.

Explanation

Let, `n` be the volume density of electrons, then from `I = rho S_(x) V_(d)`
`I = n e S_(x)| lt vec(v) gt | = n e S_(x) (l)/(t)`
So, `t = (n e S_(x) l)/(I) = 3 mu s`.
(b) Sum of electrons froces
`= | (nv) e vec(E)| = |n S l e rho vec(j)|`. where `rho` is resistivity of the material.
`= n S l epsilon rho (I)/(S) = n e l rho I = 1.0 muN`