Question

A straight conductor of uniform cross-section carried 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 velocities only, is

• A. Is
• B. I/s
• C. $\sqrt{I/s}$
• D. $(I/s{)}^2$

Answer 1

The correct option is A Is

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

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),

Vd=Is