Electric Force problem -> Infinite charged plane with hole

[moonrkr]

Electric Force problem --> Infinite charged plane with hole

The plane is infinite charged. It has a charge density (σ) of 10nC/m$^{2}$. 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$_{o}$
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>>>!

 

[mathfeel]

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

=====================================================================



MY set UP:
I was thinking about using E=σ/2*ε$_{o}$
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>>>!

Consider the hole as a combination of positive and negative charges.

 

[DiracRules]

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

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.

 

[moonrkr]

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