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Gauss's law problem

  1. Oct 16, 2004 #1
    An infinitely long solid cylinder radius R1 lies with it's central cylindrical axis lying along the x axis. it is made of a non-conducting material. It has a volume charge density that varies with readius as follows... p(r)=A.r (C/m^3)
    where A is a constant. Consider a cylindrical Gaussian surface of length L, radius r, concentric with the x axis.

    1) Derive a formula for the amount of charge enclosed by this Gaussian surface for r is greater than or equal to R1, and for r is less than or equal to R1

    2) Use gauss's Law to find an expression for the electric field as a function of r in these two regions

    3) graph the magnitude of the electric filed for these two regions.


    i would appreciate any help with this question because it is really stumping me.....Thanks!
     
  2. jcsd
  3. Oct 16, 2004 #2

    Tide

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    What exactly have you tried so far and what is your thinking?
     
  4. Oct 17, 2004 #3
    Oh wait one more thing, please post this type of question under "college level help" thank you.
     
  5. Oct 17, 2004 #4
    Solution to the Gauss law problem:

    Volume charge density= Ar
    a -> radius of cylinder
    For r > a

    Let the radius of cylindrical Gaussian surface be r

    E . 2. pi. r. l = integral {( 2*pi.A.l.r. dr / e0 ), 0 , a}

    [integral { (), ,} denotes-- () - integral funciton then the limits]

    e0 -> permittivity of free space

    [ E = A. (a^2)/ (2*r) ] ............... Solution

    For r<=a

    E . 2*pi.r.l = integral { (2*pi.A.l.r dr/ e0), 0, r}


    [ E=A.r/2 ] .............. Solution
     
  6. Oct 19, 2004 #5
    that doesn't make sense to me. Isn't the problem more complex than 2 integrals, because i got no credit for the integrals i put down, being somewhat similar to the ones you replied with.
     
  7. Oct 24, 2004 #6
    gauss law problem

    :frown: [tex]\mbox{i m sorry i forgot to divide by } \epsilon_0\mbox{. Divide the solutions by} \epsilon_0 \mbox{. I feel, that is the correct solution.}[/tex]
     
  8. Oct 24, 2004 #7
    another method

    You may also use the differential form of Gauss law for cylindrically radial field. It goes something like this:
    [tex] \frac{d(E.r)}{dr} = \frac{\rho r}{\epsilon_0} [/tex]

    Make [tex] \rho [/tex] as a function or r and integrate over proper limits.
     
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