JEE Mains · Physics · STD 12 - 1. Electric charges and fields
The region between two concentric spheres ofradii '\(a\)' and '\(b\)', respectively (see figure), have volume charge density \(\rho = \frac{A}{r}\) where \(A\) is a constant and \(r\) is the distance from the centre. At the centre of the spheres is a point charge \(Q\). The value of \(A\) such that the electric field in the region between the spheres will be constant, is :
- A \(\frac{{2Q}}{{\pi \left( {{a^2} - {b^2}} \right)}}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\)
- B \(\;\frac{{2Q}}{{\pi {a^2}}}\)
- C \(\;\frac{Q}{{2\pi {a^2}}}\)
- D \(\;\frac{Q}{{2\pi \left( {{b^2} - {a^2}} \right)}}\)
Answer & Solution
Correct Answer
(C) \(\;\frac{Q}{{2\pi {a^2}}}\)
Step-by-step Solution
Detailed explanation
Applying Gauss's law \(\oint_{\mathrm{S}} \overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{ds}}=\frac{Q}{\epsilon_{0}}\) \(\therefore \mathrm{E} \times 4 \pi \mathrm{r}^{2}=\frac{\mathrm{Q}+4 \pi \mathrm{ar}^{2}-4 \pi \mathrm{Aa}^{2}}{\epsilon_{0}}\)…
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