Magnitude of momentum of electrons

[sanalsprasad]

Homework Statement

Find the magnitude of momentum of electrons in a straight wire of copper of length 1 meter carrtying a current of 16 ampere.

a) 14.56e-12 kg m/s
b) 29.12e-12 kg m/s
c) 18.2e-11 kg m/s
d) 91e-12 kg m/s

The answer is (d)

Homework Equations

The Attempt at a Solution

16 A = 16C/s
16 A = 16 * ( 6e+18 ) electrons/s [ 1 C = 6e+18 electrons ]
= 96e+18.

mass of 96e+18 electrons/s = 9.1e-31 * 96e+18
= 8.73e-11 kg/s

Since the only unit left is meter and there is only quantity of meter(1 meter), i just multiply it to make the unit of momentum.

so i get the answer as 8.73e-11 kg m/s, which is the closest to the right answer.

But this doesn't really seem to make sense, isn't there some other way? The value for mass of an electron is also not given in our textbook.

 

[gneill]

The number of electrons in motion depends upon the charge density and volume of the material. In this case it's a copper wire, with charge density of 13.6 x 10^9 Coul/m^3.

I would suggest first making a derivation of the momentum purely symbolically, with an assumed cross sectional area for the wire, to being with. The area should drop out of the final expression, leaving a particularly simple result.

Things you'll need to know:

Charge density of copper (rho)
Charge on the electron.
Mass of the electron.
Formula for the current density, J = rho*v