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Electric field in a wire with same current as another wire

  1. Oct 25, 2016 #1
    1. The problem statement, all variables and given/known data
    For what electric field strength would the current in a 2.0-mm-diameter nichrome wire be the same as the current in a 1.0-mm-diameter gold wire in which the electric field strength is 0.0095 N/C?

    dn = .002m
    dg = .001m
    Eg = .0095 N/C

    ρn = 100 * 10-8 Ωm
    ρg = 2.44 * 10-8 Ωm

    2. Relevant equations
    V = IR
    R = ρL/A
    V = E * Δs

    3. The attempt at a solution

    First, I found a general equation for current in a wire:

    V = IR
    I = V/R
    I = (E*Δs)/(ρL/A)
    I = EA/ρ

    Then, I used this to find the current in the gold wire (and by extension, the nichrome wire).

    In = Ig = Eg * Ag / ρg

    I then used the I = EA/ρ equation to find an expression for the electric field in the nichrome wire, and plugged in the above value for the current.

    En = In * ρn / An
    En = (Eg * Ag * ρn) / (ρg * An)

    I then plugged in the values and solved.

    En = [(.0095 N/C)(π*(.001m)2/4)(100*10-8Ωm) / [(2.44*10-8Ωm)(π*(.002m)2/4)]

    = .0973 N/C

    Webassign is not accepting this answer. Does anyone know where I went wrong?
     
    Last edited: Oct 25, 2016
  2. jcsd
  3. Oct 25, 2016 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Welcome to PF!

    Your work looks correct. Did you get the values of the resistivities from you textbook?
     
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