what is the current density and electron drift speed

Question

calculate the current density and electron drift speed
given: current=8.49x10^-10, copper wire diameter=2.5mm, charge carriers er unit volume=2.49x10^28m-3. Assume that the current is uniform

Answer 1

Volume of wire=πr^2L where r=radius and L=length. If the electron drift speed=V then L=VT where T is the time for the electrons to travel the length of the wire, so volume of wire=πr^2VT. N=number of electrons per mm^3=2.49*10^28/10*9=2.49*10^19. The charge on one electron is 1.602*10^-19 coulomb approx. Current I=Q/T where Q=sum of the charges on the electrons. I=8.49*10^10 amps. Cross-sectional area of wire, A=π(1.25)^2=1.5625π=4.909sq mm. 

The charge density, D=2.49*10^19*1.602*10^-19=3.99 coulomb per mm^3. The current density is 3.99C/mm^3/sec or 3.99amps/mm^3.

I=ALQ/T=A(VT)Q/T=AVQ=4.909*3.99V.

So V=8.49*10^10/(4.909*3.99)=4.3345*10^9 mm/s=4.3345*10^6 m/s.