Force Acting on Charge on Metal Ball: Irodov Problem 3.69

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The problem involves calculating the resultant force acting on a charge located on one half of a metal ball with a radius of 1.5 cm and a charge of 10 µC. The solution requires applying Gauss's law to find the electric field (E) and then integrating the vertical component of the electric field (E_z) over the hemisphere. Key steps include determining E using Gauss's law, calculating E_z as E*cos(θ) = Q*r*cos(θ)/R^3, and integrating E_z multiplied by the charge density (ρ) over the hemisphere.

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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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You need to show your work before you get help.

Which part of the solution are you stuck in?
 
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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