Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

This is - number of charges trough

  1. Jul 23, 2006 #1
    This is urgent - number of charges trough...


    I can't figure out why the next formula tells us the number of charges that move trough cross-sectional area of the conductor.

    If a segment of wire has N charges moving with average velocity v, then in time [delta]t the number of charges is

    N * A * v * [delta]t

    A is the cross-sectional area of the conductor
    N is number of charged particles per unit volume

    thank you
  2. jcsd
  3. Jul 23, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The distance traveled by a charge in time [itex]\delta t[/itex] is, on average, [itex]v\delta t[/tex].

    Construct a plane that cuts through the wire normally. We want to count the number of electrons passing through this plane in some time [itex]\delta t[/itex]. Now, if all the electrons have velocity v, then for an electron to pass through the plane at some time t, it must have been no farther back than [itex]v\delta t[/tex] at a time [itex]t-\delta t[/itex]. In other words, only those electrons contained within the cylinder (for a wire of circular cross-section) of length [itex]v\delta t[/tex] and area A, at a time [itex]t-\delta t[/itex] will be able to pass through the wall in the ensuing time [itex]\delta t[/tex]. This number is simply the product of the volume of this cylinder, [itex]Av\delta t[/tex] and the number density, N.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook