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Electric Force problem -> Infinite charged plane with hole

  1. Oct 14, 2011 #1
    Electric Force problem --> Infinite charged plane with hole

    The plane is infinite charged. It has a charge density (σ) of 10nC/m[itex]^{2}[/itex]. If R=5cm, determine the electric force of a proton in the point P=(0,0,10cm).

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    MY set UP:
    I was thinking about using E=σ/2*ε[itex]_{o}[/itex]
    and use F=Eq.
    I can see problems in the book with the infinite charged plane, but they don't have a hole thru it... PLEASE HELP>>>!
     
  2. jcsd
  3. Oct 14, 2011 #2
    Re: Electric Force problem --> Infinite charged plane with hole

    Consider the hole as a combination of positive and negative charges.
     
  4. Oct 14, 2011 #3
    Re: Electric Force problem --> Infinite charged plane with hole

    You can face this problem at least in two ways:
    1) Calculate explicitly the force with the Coulomb expression [itex]\vec{F}=\frac{q_1q_2}{4\pi\epsilon r^2}[/itex]
    2) Solve the problem "geometrically": how do you build a charged plane with a hole? You can think either [itex]\vec{F}_{positively\,charged\,plane\,with\,hole}=\vec{F}_{positively\,charged\,plane\,without\,hole}-\vec{F}_{field\,of\,the\,hole}[/itex] or [itex]\vec{F}_{positively\,charged\,plane\,with\,hole}=\vec{F}_{positively\,charged\,plane\,without\,hole}+\vec{F}_{negatively\,charged\,hole}[/itex]

    Both ways, you should be careful, because the symmetry of the problem allows you to do powerful simplifications on the components of the forces acting on the proton.
     
  5. Oct 14, 2011 #4
    Re: Electric Force problem --> Infinite charged plane with hole

    Force of the hole - Force of the plane (without hole) = Force of the entire setting(plane with hole)?
     
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