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How do I prove that Gauss's Law works and is valid for a sphere with a circular disk on top? I'm given the radius of the sphere R(00, π), radius of the disc (R sin 0o), the center of the circular disc: z = 20 = R sin 00 and the differential area element for both the sphere (e-R sin 00) and the circular disc (ezs dsdo). Where: Various forms of Gauss's law: S = = √r² - z² With (0, 2) and e,ex = cos 0. So far, I have only placed the integral equations regarding Gauss's Law: Electric flux through a closed surface Magnitude of electric field E z² for for s(0, e,R sin 00) - ¹₁ = f Écoso dª = f £¸dª = fẼ · dà = ΦΕ dA Angle between E and normal to surface Component of E perpendicular to surface Element of surface area Total charge enclosed by surface Qencl €0 Vector element of surface area Electric constant (22.9) I also consulted other resources and they said that the equation for the sphere should be utilized, so that everything is simplified. I also saw sources using the steradian method, however, my professor strictly wants me to use the differentials provided. I'm at a dead end, because most sources together with my lectures only cover examples using symmetric figure.