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 Flux thru the top face of a cube

  1. Jan 26, 2013 #1
    1. The problem statement, all variables and given/known data
    An electric field given by [tex]\vec E = 4.0 \hat i - 3.0(y^2+2) \hat j[/tex] pierces a 2.0 meter by 2.0 meter by 2.0 meter cube. What is the electric flux thru the top face?

    2. Relevant equations
    [tex]\phi = \int \vec E \cdot d \vec A[/tex]

    3. The attempt at a solution
    I'm aware that you can take a shortcut to solving this problem by considering that the electric field at y = 2.0 is a constant [tex]\vec E = 4.0 \hat i - 3.0([2.0]^2+2) \hat j = 4.0 \hat i - 18.0 \hat j[/tex].

    then this leads to, [tex]\phi = \int \vec E \cdot d \vec A = \vec E \int d \vec A = \vec E \cdot \vec A[/tex]

    And since [tex]\vec A[/tex] has no x-component, we only need to consider the y component. The area of the top face is just 2 times 2.

    [tex]\phi = -18.0 * (2^2) = -72 \frac{Nm^2}{C}[/tex]

    But how do I solve this same problem without taking the shortcut?

    2. Relevant equations???
    Evaluating a flux integral (surface is oriented upward):
    [tex]\int_S \int \vec F \cdot \vec N dS[/tex]

    The unit vector normal to the surface:
    [tex]\hat N dS = \frac{\bigtriangledown g(x,y,z)}{||\bigtriangledown g(x,y,z)||} dS = \bigtriangledown g(x,y,z) dA[/tex]

    4. The attempt at a solution without the shortcut
    The surface is probably given by [tex]z = g(x, y) = y - 2[/tex]
    [tex]\hat N dS= dA \hat j[/tex]
    [tex]\phi = \int_S \int \vec E \cdot \vec N dA = \int_R \int [4.0 \hat i - 3.0(y^2+2) \hat j] \cdot [dA \hat j] = \int_R \int -3.0(y^2+2)dA = -3.0 \int_0^2 \int_0^2 (y^2+2) dxdy = -40.0[/tex]

    :( this is obviously the wrong answer, any clue on what i'm doing wrong?

    Thanks in advance!
    Last edited: Jan 26, 2013
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted