Question

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 conductor, due to their drift velocities only is?

Answer 1

I = nAeVd  where n = no. of electrons per unit volume, A= area of cross section of the wire , e = charge of an electron , Vd = drift velocity

what we want is momentum per unit length of wire.(ie) mVd , where m is the total mass of all electrons in the unit length of wire. here  I = (q/t) = nAeVd . and m = n*(A*1)*(me). As n = no. of electrons per unit volume and A*1 is the volume of the unit length cross section and me is the mass of one electron.

Therefore mVd  = (nAVd)*me = (q*me)/(t*e)

As e/me = specific charge  = s,

mVd  = q/(t*s)