(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi guys, I have this problem but I sure what I did is wrong:

A uniformly charged hemi-sphere of radius a, surface density N, is situated in the upper half space (z>=0). The center field of the hemi-spere coincides with the center of the coordinate system. Find the electric field vector at the origin.

2. Relevant equations

E=k*N*dS/R^2

where k=1/(4pi*epsilon_0)

3. The attempt at a solution

What I did is this:

The z-component of the vector is:

dE=k*( N* dS*cos(x))/R^2

where k=1/4*pi*epsilon0)

and dS=R^2*sin(x)dx d(phi)

where x is the vertical angle often called theta

then:

dE=(N*R^2*sin(x)*cos(x)*dx*d(phi))/R^2

My problem is that, before integration, the R^2 cancel out and I have an expression of the electric field without R or z(coordinate)

Can someone help me please?

Thanks

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# Electri field and hemi-sphere

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