A straight conductor of uniform cross section carries a time varying current, which varies at the rate dI//dt = I. If s is the specific charge that is carried by each charge carries of the conductor and l is the length of the condcutor, then the totalt force experienced by all the charge carries per unit length of the conductor due to their drift velocities only is

Options

A. `F = I s`
B. `F = (I)/(2sqrtls)`
C. `F = (I)/(s)`
D. `F = (2I l)/(s)`

Answer

C

Explanation

Momentum of each charge carrier moving with a drift velocity
v is mv. Total number of charge carries in the sample is
N = n (Al), where n is the number of charge carries per unit
volume and A is area of cross section of the conductor.
Total momentum is p = N(mv)=nAlmv
Further, we have
`upilon = I//"ne"A`
or `P = nAim((I)/(meA)) = l((M)/(e))I`
Since `F = (dp)/(dt)`
or `F=(l)/(S) I or (F)/(l) = (I)/(s)` [ `:.` specific charge = e/m]