JEE Mains · Physics · STD 12 - 1. Electric charges and fields
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
- A \(a = \frac{{3R}}{{{2^{1/4}}}}\)
- B \(a = {2^{ - 1/4}}R\)
- C \(a = {8^{ - 1/4}}R\)
- D \(a = R/\sqrt 3 \)
Answer & Solution
Correct Answer
(C) \(a = {8^{ - 1/4}}R\)
Step-by-step Solution
Detailed explanation
\(E 4 \pi a^{2}=\frac{\int_{0}^{\theta} k r 4 \pi r^{2} d r}{e_{0}}\) \(E=\frac{k 4 \pi a^{4}}{4 \times 4 \pi \varepsilon_{0}}\) \(2 \mathrm{Q}=\int_{0}^{\mathrm{R}} \mathrm{kr} 4 \pi \mathrm{r}^{2} \mathrm{dr}\) \(\mathrm{k}=\frac{2 \mathrm{Q}}{\pi \mathrm{R}^{4}}\)…
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