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Charge and excess electrons

  1. Jan 26, 2017 #1
    1. The problem statement, all variables and given/known data
    A charged nonconducting rod, with a length of 1.33 m and a cross-sectional area of 3.40 cm2, lies along the positive side of an x axis with one end at the origin. The volume charge density ρ is charge per unit volume in coulombs per cubic meter. How many excess electrons are on the rod if ρ is (a) uniform, with a value of -4.22 µC/m3, and (b) nonuniform, with a value given by ρ = bx2, where b = -2.66 µC/m5?


    2. Relevant equations
    q=ne
    p=bx^2

    3. The attempt at a solution
    So for part a:
    n=(p(a)L)/e
    n=(-4.22E-6C)(3.4E-4m^2)(1.33m)/(-1.6E-19C)
    n=1.193E10 electrons

    Part b is where i was incorrect
    p=bx^2
    p=-2.66x^2
    dq=Apdx
    =3.4E-4*-2.66x^2dx
    so q=9.04E-4* the integral of x^2dx from 0 to 1.33
    q=-7.09E-4C
    n=q/e
    =-7.09E-4C/-1.6E-19C
    =4.431E15 electrons<----- this was incorrect and I am unsure of my mistake
     
  2. jcsd
  3. Jan 26, 2017 #2

    gneill

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    Staff: Mentor

    Looks like the order of magnitude went astray starting here. 10-4 is too big. Check the units of the constant b.
     
  4. Jan 30, 2017 #3
    Right, so multiply the final answer by the conversion factor of microcoulombs to coulombs of E-6.
     
  5. Jan 30, 2017 #4

    gneill

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    Staff: Mentor

    That'll work.
     
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