A uniform solid non conducting sphere contains uniformly distributed charge Q. Consider the shown section at a perpendicular distance R2 from centre of the shown uniform solid sphere. Electric flux through the section is Qk2 ε0. Find the value of k.

Let’s construct a cone as shown. By field picture, ϕ through lateral surface zero.⇒ϕsection=ϕcone=qinsideε0=ρ.13πR2(R2)ε0=(Q43πR3).(13πR322)ε0=Q82ε0

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A uniform solid non conducting sphere contains uniformly distributed charge Q. Consider the shown section at a perpendicular distance $\frac{R}{\sqrt{2}}$ from centre of the shown uniform solid sphere. Electric flux through the section is $\frac{Q}{k \sqrt{2} ε_{0}} .$ Find the value of $k$ .

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Let’s construct a cone as shown. By field picture, $ϕ$ through lateral surface zero.

$\Rightarrow ϕ_{\sec t i o n} = ϕ_{c o n e} = \frac{q_{i n s i d e}}{ε_{0}}$

$= \frac{ρ . \frac{1}{3} π R^{2} (\frac{R}{\sqrt{2}})}{ε_{0}}$

$= \frac{(\frac{Q}{\frac{4}{3} π R^{3}}) . (\frac{1}{3} π \frac{R^{3}}{2 \sqrt{2}})}{ε_{0}} = \frac{Q}{8 \sqrt{2} ε_{0}}$

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