Dielectric Gauss

A sphere of radius \(R\) has half part filled with di-electric of permittivity \(\epsilon\) and the other part is vacuum (As shown in diagram). The electric field strength in vacuum is \(E\) and the vector \(E\) is making angle \(\theta\) with the normal \(N\) to the dielectric.

The spherical surface is of negligible thickness.

What is the flux of vector \(E\) through the sphere with centre at \(O\) (See diagram).

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