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Line Charge and Charged Cylindrical Shell (Gauss law)

  1. Jan 30, 2014 #1
    1. The problem statement, all variables and given/known data
    An infinite line of charge with linear density λ1 = 6.2 μC/m is positioned along the axis of a thick insulating shell of inner radius a = 2.7 cm and outer radius b = 4.4 cm. The insulating shell is uniformly charged with a volume density of ρ = -552 μC/m3.


    1) What is λ2, the linear charge density of the insulating shell?
    -2.093 μC/m
    2) What is Ex(P), the value of the x-component of the electric field at point P, located a distance 7.5 cm along the y-axis from the line of charge?
    0 N/C

    3) What is Ey(P), the value of the y-component of the electric field at point P, located a distance 7.5 cm along the y-axis from the line of charge?

    2. Relevant equations



    3. The attempt at a solution

    number 3 is the one I am stuck on. I used gauss law and ended with the equation E(x)=landa/(2pi (8.85*10^-12 * r) and got 503541.06 N/C but it seems to be wrong.
     
    Last edited: Jan 30, 2014
  2. jcsd
  3. Jan 30, 2014 #2

    haruspex

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    I get nearly double that. Please post your working.
     
  4. Jan 30, 2014 #3

    BruceW

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    ah! you beat me to it haruspex
     
  5. Jan 30, 2014 #4
    I used gauss law
    integral(E*dA)=q_in/epsilon
    LHS E∫dA RHS ∫(from 0 to h) (λ1*dz)/(ε0)
    2pi*dx*h*E= (λ1*h)/ε0
    E=λ/(2*∏*ε0*dR)
     
  6. Jan 30, 2014 #5

    haruspex

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    Yes, those are the equations, but I asked to see the working. can't tell where you're going wrong without that. you are adding the fields for the two charges, right?
     
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