At room temperature, copper has free electron density of `8 . 4 xx 10^(28)m^(-3)` . The electron drift velocity in a copper conductor of cross-sectional area of `10^(-6)m^(2)` and carrying a current of 5.4 A , will be

Options

A. `4 m-s^(-1)`
B. `0.4 m-s^(-1)`
C. `4 cm -s^(-1)`
D. `0.4 mm-s^(-1)`

Answer

D

Explanation

Given : Electron density
`(n_(e)) = 8.4 xx 10^(28) m^(-3)`
Cross-sectional area of conductor
`(A) = 10^(-6) m^(2)` and
Current (I)= 5 .4 A
We know that drift velocity of free electrons in a copper conductor
`(u_(d)) = (I)/(n_(e)A)`
`=(5.4)/((8.4 xx 10^(28))xx(1.6xx10^(-19))xx10^(-6))`
`=(5.4)/(8.4 xx1.6 xx 10^(3))`
`= 0.4 xx 10 ^(-3) m.s^(-1) =0 . 4 mm-s^(-1)`
(where e = charge on electron equal to `1.6 xx 10^(-19) C ` )