Dielectric Gauss

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

The spherical surface is of negligible thickness.

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


The answer is 0.00872222.

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