A straight copper-wire of length `100m` and cross-sectional area `1.0mm^(2)` carries a current `4.5A`. Assuming that one free electron corresponds to
A straight copper-wire of length `100m` and cross-sectional area `1.0mm^(2)` carries a current `4.5A`. 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 electrostatic forces acting on all free electrons in the given wire. Given resistivity of copper is `1.72xx10^(-8)Omega-m` and density of copper is `8.96g//cm^(3)`.
A. The time taken by an electron to displace from one end of the wire to the other is 4 x 106 s.
B. The sum of electric force acting on all free electrons in the given wire is 1 x 106 N.
C. The time taken by an electron to displace from one end of the wire to the other is 3 x 106 s.
D. Both (b) and (c).
1 Answers
Correct Answer - D
Every copper atom ahs one free electron. So, number per unit volume=number of atoms per unit volume.
`therefore n=(N_(a)d)/(M),d="density of copper"`
`=(6.02xx10^(23)xx8.96xx10^(3))/(63.5xx10^(-3))`
`=8.49xx10^(28)"electron per m"^(3)`
We know that, `I="ne" Av_(d)="ne"A(l)/(t)`
`t=("neAl")/(I)=(8.49xx10^(28)xx1.6xx10^(-19)xx10^(-6)xx10^(3))/(4.5)`
`=3xx10^(6)s`
Sum of electric forces
`f=|(nV)ebar(E)|=|nAlrhobarj|="nAle"rho(I)/(A)="nle"rhoI`
`=1.03xx10^(6)N`