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Homework Help: Potential of Concentric Cylindrical Insulator and Conducting Shell

  1. Sep 10, 2011 #1
    An infinitely long solid insulating cylinder of radius a = 5.3 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 45 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 14.2 cm, and outer radius c = 16.2 cm. The conducting shell has a linear charge density λ = -0.42μC/m.

    1)What is Ey(R), the y-component of the electric field at point R, located a distance d = 44 cm from the origin along the y-axis as shown?

    2)What is V(P) – V(R), the potential difference between points P and R? Point P is located at (x,y) = (44 cm, 44 cm).

    E = Qenc/[itex]\epsilon[/itex]
    E = [2k([itex]\lambda[/itex](cylinder) + [itex]\lambda[/itex](shell))]/r

    [itex]\lambda[/itex]c = [itex]\rho[/itex]*A
    = [itex]\rho[/itex]*2[itex]\pi[/itex]*0.053*0.044
    = 7.0*10^-6 C/m

    E = (2*(8.99*10^9)*(7.0*10^6+(-4.2*10^-7)))/0.44m
    = 268883 N/C

    But that answer is not correct. Please help me! I would appreciate detailed explanation or work, thank you!
  2. jcsd
  3. Sep 11, 2011 #2


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    Homework Helper

    Surely you don't mean you want someone here to do the work for you?

    Anyway, I see several errors in your calculation:
    That formula is not correct, as you could see if you check the units
    What's k? If you're using [itex]k = \frac{1}{4\pi\epsilon_0}[/itex], then I don't see how you get that formula.

    That line seems right (assuming you meant the c to be a subscript, not a variable on its own)
    but that line is not. Hint: what's the area of a circle? (What does the variable A physically represent?)
  4. Sep 11, 2011 #3


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    I think A is supposed to be the cross section of the inner cylinder, and ρ its radius. So why ρ*2π? and what is 0.044?

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