A circular disc of radius R carries surface charge density σ$$(r)=$$σ$$01$$−rR, where σ$$0$$ is a constant, and 𝑟 is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is ϕ$$0$$. Electric flux through another spherical surface of radius $$R4$$ and concentric with the disc is ϕ. Then the ratio ϕ$$0$$ϕ $$is_________$$

Question

A circular disc of radius R carries surface charge density  σ$$(r)=$$σ$$01$$−rR, where σ$$0$$ is a constant, and 𝑟 is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is ϕ$$0$$. Electric flux through another spherical surface of radius $$R4$$ and concentric with the disc is ϕ. Then the ratio ϕ$$0$$ϕ $$is_________$$

Infinity Learn · Accepted Answer

ϕ$$0=$$∫dqε$$0=$$∫$$0R$$ σ$$01$$−$$rR2$$$$π$$rdrε$$0$$ϕ$$=$$∫dqε$$0=$$∫$$0R/4$$ σ$$01$$−$$rR2$$$$π$$rdrε$$0$$∴ ϕ$$0$$ϕ$$=$$σ$$02$$π∫$$0R$$ r−$$r2Rdr$$σ$$02$$π∫$$0R/4$$ r−$$r2Rdr=R22$$−$$R23R232$$−$$R23$$×$$64=325=6.40$$

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