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A system consists of a uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density $ρ = \frac{α}{r}$ , where $α$ is a positive constant and $r$ is the distance from the centre of the sphere. Find the charge of the sphere for which the electric field intensity E outside the sphere is independent of R.

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$\frac{α}{2 ε_{_{0}}}$

$\frac{R^{2}}{π α}$

$\frac{2}{α ε_{_{0}}}$

$2 π α R^{2}$

answer is C.

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Detailed Solution

$E \times 4 π r^{2} = \frac{1}{\in_{0}} [q + \int_{R}^{r} \frac{α}{r} 4 π r^{2} d r$

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