A straight conductor of uniform cross-section carries a current `I`. Let `s=` specific charge of an electron. The momentum of all the free electrons per unit length of the conductor, due to their drift velocity only, is

Options

A. `i.s`
B. `sqrt(i)//(s)`
C. `i/s`
D. `(i/s)^(2)`

Answer

C

Explanation

Current flowing in a straight conductor
`i="nAev"_(d)` or `v_(d)=(i)/("nAe")`
Total number of free electrons in the unit length of conductor, `N = nA xx l = nA xx 1` (length, l = 1m). Total linear momentum of all the free electrons per unit length `= N_(m)v_(d)=nAm xx (i)/("nAe")=(i0)/((e//m))=(i)/(s)`
where, s is charge per unit mass (e/m).