1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Electric Field

  1. Sep 14, 2006 #1
    check whether this result of this problem is consistent with this statement
    [tex] \vec{E_{above}} - \vec{E_{below}} = \frac{\sigma}{\epsilon_{0}} \hat{n} [/tex]

    an infinite plan carries a uniform surface charge sigma. Find its electric field

    Draw a Gaussian Pillbox extending above and below the plane. Then
    since [tex] \oint \vec{E} \bullet d\vec{a} = \frac{Q_{enc}}{\epsilon_{0}} [/tex]

    and since[tex]Q_{enc} = \sigma A [/tex]

    By Symmetry E points up and down

    [tex] \int \vec{E} \bullet d\vec{a} = 2A |\vec{E}| [/tex]

    so [tex] \vec{E} = \frac{\sigma}{2\epsilon_{0}} \hat{n} [/tex]

    Now to tackle the question

    Well for an infinite sheet for each side the Electric field points normal to the sheet, right?
    SO the electric field for the top is [itex] \vec{E} = \frac{\sigma}{\epsilon_{0}} \hat{n} [/itex]
    and te bottom is the negative of that

    So when you add those two together you get [tex] \vec{E} = \frac{\sigma}{\epsilon_{0}} \hat{n}[/tex]

    and this is consistent with statement. Easy enough. i just want to know whether this kind of 'proof' for the statement is satisfactory.
  2. jcsd
  3. Sep 16, 2006 #2
    yeah that's right.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook