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Question: Answered & Verified by Expert
A hollow spherical shell of radius $r$ has a uniform charge density $\sigma$. It is kept in a cube of edge $3 r$ such that the centres of the cube and the shell coincide. Then the electric flux coming out of one face of a cube is ( $\varepsilon_0$ - permittivity of free space)
PhysicsElectrostaticsTS EAMCETTS EAMCET 2023 (14 May Shift 2)
Options:
  • A $\frac{\pi \mathrm{r}^2 \sigma}{\varepsilon_0}$
  • B $\frac{5 \varepsilon_0}{2 \pi r^2 \sigma}$
  • C $\frac{\pi \mathrm{r}^2 \sigma}{6 \varepsilon_0}$
  • D $\frac{2 \pi r^2 \sigma}{3 \varepsilon_0}$
Solution:
2203 Upvotes Verified Answer
The correct answer is: $\frac{2 \pi r^2 \sigma}{3 \varepsilon_0}$
Charge on the hollow sphere, $q=\sigma \times 4 \pi r^2$
According to Gauss's law, The flux through a single face
of the cube, $\oint^{\prime}=\frac{1}{6} \frac{\mathrm{q}}{\varepsilon_0}=\frac{\sigma \times 4 \pi \mathrm{r}^2}{6 \varepsilon_0}=\frac{2 \pi \mathrm{r}^2 \sigma}{3 \varepsilon_0}$

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