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Homework Help: Gauss' Law With an Infinite Cylinder of Charge

  1. Oct 27, 2007 #1
    [SOLVED] Gauss' Law With an Infinite Cylinder of Charge

    1. The problem statement, all variables and given/known data

    The test question was to find the potential difference between a point S above a cylinder of charger per length lambda, and a point on the surface of the cylinder having radius R and infinite length.

    2. Relevant equations

    Stupid me tried to grind through it during the test. But looking at the prof's solution:


    Here's the test if you need to know the question how he worded it:


    Problem #1.

    I don't get how he got "E(s)*2pi*L*S

    I get the 2pi and L come from integrating over phi and the length of the cylinder, but I can't figure out where that S came from.

    Is it because you'd need a cosine(theta) for the direction that the cylinder is from S? Where cosine is S/distance? Then wouldn't he have to add in a bunch of other stuff? I'm just not seeing something here and I feel embarrassed.
  2. jcsd
  3. Oct 27, 2007 #2
    [tex]\int E \cdot dA = EAcos(\Theta)[/tex]

    Where [tex]\Theta[/tex] is the angle between the surface of the cylinder and the electric field.

    Now, simplify this last expression. What is A? What is [tex]\Theta[/tex]?
  4. Oct 27, 2007 #3
    Ohhhhhh I get it. A is 2pi*Length*radius, and he's just using S as the radius, since it shouldn't matter.

    Gotcha, thanks a bunch.
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