Let a total charge \(2Q\) be distributed in a sphere of radius \(R\), with the charge density given by \(\rho(r) = kr\), where \(r\) is the distance from the centre. Two charges \(A\) and \(B\), of \(-Q\) each, are placed on diametrically opposite points, at equal distance, \(a\), from the centre. If \(A\) and \(B\) do not experience any force, then

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Answer & Solution

Correct Answer

(C) \(a = {8^{ - 1/4}}R\)

Detailed explanation

\(E 4 \pi a^{2}=\frac{\int_{0}^{\theta} k r 4 \pi r^{2} d r}{e_{0}}\)

\(E=\frac{k 4 \pi a^{4}}{4 \times 4 \pi \varepsilon_{0}}\)

\(2 \mathrm{Q}=\int_{0}^{\mathrm{R}} \mathrm{kr} 4 \pi \mathrm{r}^{2} \mathrm{dr}\)

\(\mathrm{k}=\frac{2 \mathrm{Q}}{\pi \mathrm{R}^{4}}\)

\(\mathrm{QE}=\frac{1}{4 \pi \varepsilon_{0}} \frac{\mathrm{QQ}}{(2 \mathrm{a})^{2}}\)

\(\mathrm{R}=\mathrm{a} 8^{1 / 4}\)

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