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Several Questions on Electric Potential

  1. Jul 13, 2004 #1
    Hey everyone, I just wanted to ask these two questions on electric potential that are having me a bit stuck:

    A thin rod of length 2L is centered on the x axis on a coordinate plane... The rod carries a unif. distr. charge Q. Determine the potential V as a funct of y for the points along the Y axis.

    My problem with this--- its not an infinite rod!! I understand that since this rod is of specified length, we will have to some tricky math here and end up doing an integral with our limits for the rod (IE -L and L)... but would all this be is essentially the equation one can derive for the same situation for ELECTRIC FIELD, and just multiply by r? (Where r is the dist on the y axis)

    Another Question is suppose a conducting sphere of diameter d is charged to a certain voltage V relative to V = 0 at r = infinity.

    How can we find an equation sets up the surface charge density sigma?
    (Just in general)

    I appreciate any help thanks.
  2. jcsd
  3. Jul 14, 2004 #2
    Electric Field:

    [tex] \def\vr{\mathord{\vec r}} \providecommand{\abs}[1]{\lvert #1 \rvert}
    \vec E (\vr) = \frac{1}{4 \pi \epsilon_0}\int\frac{\rho(\vr\ ')(\vr-\vr\ ')}{\abs{\vr-\vr\ '}^3}d l'[/tex]

    Electric potential:
    \def\vr{\mathord{\vec r}} \providecommand{\abs}[1]{\lvert #1 \rvert}
    &\phi(\vr)=\frac{1}{4\pi\epsilon_0}\int \frac{\rho(\vr\ ')}{\abs{\vr-\vr\ '}}d l '[/tex]

    And for the 2nd prob

    [tex] E_{outside shell} - E_{inside shell} = \frac {\sigma}{\epsilon_0} \vec n[/tex]

    Where n is the unit normal vector pointing out of the shell
  4. Jul 14, 2004 #3
    Excellent that first one makes perfect sense now--- thank you.
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