Saved Bookmarks
| 1. |
Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1.0 xx 10^(-7) m^(2) carrying a current of 1.5 A. Assume that each copper atom contributes roughly one conduction electron. The density of copper is 9.0 xx 10^(3) kg//m^(3) and its atomic mass is 63.5 u. |
|
Answer» SOLUTION :(a) The direction of drift velocity of conduction electrons is opposite to the electric field direction, i.e., electrons drift in the direction of increasing potential. The drift speed `u _(d)` is given by `u _(d) =(l//n eA)` No, `e = 1.6 xx 10 ^(-19) C, A = 1.0 xx 10^(-7) m ^(2).I = 1. 5 A.` THe density of conduction electrons, n is equal to the number of atoms per cubic meter (assuming one conduction enectron per Cu atom as is reasonable from its valence electron count of one). A cubic metre of copper has a mass of `9.0 xx 10 ^(3)Kg.` Since `6.0xx 10^(23)` copper atoms have a mass of `63.5g.` `n = (6.0 xx 10 ^(23))/(63.5) xx 9.0 xx 10 ^(6)` ` = 8.5 xx 10 ^(28) m^(-3)` which gives, `u _(d) = ( 1.5)/(8.5 xx 10 ^(28) xx.16 xx 10 ^(-19) xx 1.0 xx 10 ^(-7))` `=1.1 xx 10 ^(-3) ms ^(-2) =1.1 mm s ^(-1)` (b) (1) At a temperature T.the thermal speed of a copper atom of mass M is obyained from` [ lt (1//2) Mv ^(2)gt = (3//2) K _(B) T]` and is THUS typically of the order of `sqrt (k_(B) T//M).` where `k _(B)` is the Boltzmann constant. For copper at 300 K. this is about `2 xx 10 ^(2)` m/s. This FIGURE indicates the random vibrattonal speeds of copper atoms in a conductor. Note that the drift speed of electrons is much smaller, about `10 ^(-5)` times the tpyical thermal speed at ORDINARY temperatures. (i) An electric field travelling along the conductor has a speed of an electronagetic wave, namely equal to `3.0 xx 10 ^(8) m s ^(-1)`The drift speed is, in comparison, extremely small, smaller by a factor of `10 ^(-11).` |
|