Force Acting on Charge on Metal Ball: Irodov Problem 3.69

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A metal ball or radius R=1.5[cm] has a charge q=10e-6[C]. Find the modulus of the vector of the resultant force acting on a charge located on one half of the ball.

I found a solution on http://irodov.nm.ru/3/resh/3_69.gif but I don't understand explanations regardind to the problem so I would appreciate if anyone could explain a solution.
 

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The whole problem is a little bit fuzzy to me (E', Eokp, E and relations between them), so it would be very helpful if you could explain main steps in solving this problem (without doing integration, just basic steps and formulae).

Thanks.
 
-marko- said:
A metal ball or radius R=1.5[cm] has a charge q=10e-6[C]. Find the modulus of the vector of the resultant force acting on a charge located on one half of the ball.
1. Find E using Gauss's law.
2. E_z=Ecos\theta=Qrcos\theta/R^3.
3. Integrate E_z\rho over the hemisphere.
 
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