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Homework Help: Electric field between inner and outer cylinder

  1. Mar 3, 2016 #1
    1. The problem statement, all variables and given/known data
    A capacitor is constructed of two long concentric metal cylinders, each having length of 1.0 meters. The inner cylinder has a radius R1 = 1.0 cm, and the outer cylinder has a radius R2 = 1.25 cm. The hollow space between the two cylinders is filled with nylon having a dielectric constant of 4.0. A charge of Q =5 nC is transferred from the inner cylinder to the outer shell. (a) Find the field between the two using Gauss's law, and use the computer to make a graph of the magnitude of the electric field E(r) from r = 0.5 cm to r = 1.5 cm.

    2. Relevant equations
    E = q/εA

    3. The attempt at a solution
    The field on the inner cylinder would be E = 8990 N/C and the field on the outer cylinder would be 7190 N/C. I am confused though because it is asking for an electric field between the plates. Do they just want an equation for the field based on r? For the graph part I assume they want an equation, but when r < 1 or r > 1.25 the field would be zero right? I just don't totally understand the question, so any input regarding what you think my professor wants would be appreciated.

    I am also assuming the cylinders have no top or bottom.
  2. jcsd
  3. Mar 3, 2016 #2

    Charles Link

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    Homework Helper
    Gold Member

    To begin, first work the problem without any dielectric between the cylinders. A charge per unit length Q/L gives a radially outward electric field (using Gauss's law M.K.S. units) obeying ## E(r)*2*\pi*r*L=(Q/L)/\epsilon_o)*L ## ==>> ## E(r)=(Q/L)/(2\pi*r\epsilon_o) ## The dielectric will reduce this E(r) by a factor of the dielectric constant ## \epsilon ##. The electric field is zero outside of the region ## 1.0 cm<r<1.25 cm ## In doing the calculations, be sure to have "r" expressed in meters.
  4. Mar 3, 2016 #3
    What exactly do you want to know? If, whether the field for r less than 1, or greater than 1.25cm is zero, then yes, it would be.
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