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Potential energy for a dipole between 2 infinitely large charged sheets

  1. Sep 24, 2011 #1
    1. The problem statement, all variables and given/known data
    A dipole consisting of charges +/- e 220 nm apart is placed between two very large (essentially infinite) sheets carrying equal but opposite charge densities of 125 uC/m^2.

    a) What is the maximum potential energy this dipole can have due to the sheets, and how should it be oriented relative to the sheets to attain this value?

    b) What is the maximum torque the sheets can exert on the dipole, and how should it be oriented relative to the sheets to attain this value?

    c) What net force do the two sheets exert on the dipole?

    2. Relevant equations
    U = -pEcos([itex]\phi[/itex])
    p = qd
    E = [itex]\lambda[/itex]/2[itex]\pi[/itex][itex]\epsilon[/itex]x
    where [itex]\lambda[/itex] is the linear charge density, [itex]\epsilon[/itex] is the permittivity of free space, and x is a distance for a point P from the sheet.
    [itex]\sigma[/itex] = q/A (surface charge density)

    3. The attempt at a solution
    I can see from the start that once I acquire a) the rest of the question should go smoothly. Where I am stuck is trying to calculate the initial electric field between the infinite sheets that the dipole lies in. What I tried to do was first find the linear charge density from the given surface density, arriving at a value of 11.2 uC/m by simply taking the square root of the 125 uC/m^2.

    Next I treated each sheet as essentially lying where the point charges of the dipole lie (aka giving a distance of 220 nm between each sheet). With the distance found I then plugged this along with all other needed values into the electric field equation provided (the equation for the electric field strength for a point P a distance x away from an infinitely large sheet I found in my textbook).

    From there I then multiplied this value by the dipole moment to arrive at an answer of 3.22 x 10^-14 J for the potential energy. I already know for maximum potential energy the dipole should be oriented so that its negative charge faces the negatively charged sheet (dipole moment should be in the opposite direction of the electric field, giving an angle of 180 to make cos[itex]\phi[/itex] = -1 and thus cancel out the negative from the potential energy equation). My concern is that I think I am making too many assumptions (ex. about the distance between the two sheets) and am ultimately calculating the external electric field wrong. If someone could tell me if I am right or wrong, and if wrong point me in the right direction it would be greatly appreciated.
  2. jcsd
  3. Sep 24, 2011 #2
    I think you are calculating the electric field between the two sheets wrong? What is that equation [itex]E = \lambda / 2 \pi \epsilon x[/itex] ? That's not the equation for the electric field between infinite parallel sheets.

    You can find the electric field due to an infinite charged sheet by using the Gauss law. Then you can find the electric field between two of them by adding the components of the electric field made by each one of the sheets.
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