# 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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