उत्तर: (4)

समाधान:

$ \begin{aligned} Q_1 & = \sigma ,(4 \pi R^{2}) \ & = 4 \pi R^{2} \sigma \end{aligned} $

$ \begin{aligned} Q_2 & = \sigma ,(8 \pi R^{2}) \ & = 8 \pi R^{2} \sigma \end{aligned} $

$ \frac{Q_1}{4 \pi \varepsilon_0 R}=\frac{Q_2}{4 \pi \varepsilon_0(2 R)} $

$\therefore Q_2^{\prime}=2 Q_1^{\prime}$

$Q_1^{\prime}+Q_2^{\prime}=Q_1+Q_2$

$\therefore \frac{Q_2^{\prime}}{2}+Q_2^{\prime}=20 \pi R^{2} \sigma$

$\frac{3}{2} Q_2^{\prime}=20 \pi R^{2} \sigma$

$\therefore \frac{Q_2^{\prime}}{4 \pi(2 R)^{2}}=\frac{2}{3} \cdot \frac{20 \pi R^{2} \sigma}{16 \pi R^{2}}$

$\therefore \frac{\sigma^{\prime}}{\sigma}=\frac{5}{6}$