Question

2) The number density of conduction electrons in silver is 5.86 x 1028 m-3.   independent of temperature. If a cylindrical wire of length L and cross-sectional area A were made of silver its electrical resistance would be given by R= ρ L A where ρ is the resistivity of the material measured in Ω−m. The resistivity can also be shown to be related to microscopic properties of the metal such as the number density of conduction electrons, the mass and charge of the electron and the mean free time between collisions: ρ = m e2n τ .
a) Look up the resistivity of silver and use it to determine the mean free time in between collisions for electrons in silver (probably at 20˚C). Now imagine a wire with circular crosssection made of silver. A uniform electric field given by E=−0.5N Cˆ i extends across the interior of the wire (see below).

Determine the drift velocity vector for the electrons in the wire. Express this result in unit vector notation. b) Imagine a circular cross-section of the wire at point A in the diagram. If the wire has a diameter of 1 mm, what will be the net flux of electrons through that cross-section (see previous question and related handout)? Which is greater of the two quantities that comprise the net flux, the left to right flux of electrons or the right to left flux? Explain your reasoning. How much electric current flows in the wire under these conditions. c) If the wire is 0.7 m long, determine its resistance and the Joule heating rate in the wire.
  

Answer 1