A point charge q is placed on the apex of a cone of semi-vertex angle `theta`. Show that the electric flux through the base of the cone is `q(1-costheta)//2epsilon_0`.
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Explanation

Let R=slant length of cone=radius of Gaussian sphere
`:.S_0=` area of whole sphere `=(4piR^2)`
S=area of sphere below the base of the cone
`=2piR^2 (1-costheta)`
`:.` The desired flux is `phi=(S/S_0).q/epsilon_0`
`((2piR^2)(1-costheta))/((4piR^2)).q/epsilon_0`
`=(q(-costheta))/(2epsilon_0)`