JEE Mains · Physics · STD 12 - 2. Electric potential and capacitance
Two metal spheres of radius \(R\) and \(3 R\) have same surface charge density \(\sigma\). If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes \(\sigma_1\) and \(\sigma_2\), respectively. The ratio \(\frac{\sigma_1}{\sigma_2}\) is ________.
- A \(\frac{1}{9}\)
- B 9
- C \(\frac{1}{3}\)
- D 3
Answer & Solution
Correct Answer
(D) 3
Step-by-step Solution
Detailed explanation
For conducting sphere, \(\mathrm{V}=\frac{\sigma \mathrm{r}}{\varepsilon_0}\) After contact, \(\mathrm{V}_1=\mathrm{V}_2\) \(\begin{aligned} & \sigma_1 r_1=\sigma_2 r_2 \\ & \frac{\sigma_1}{\sigma_2}=\frac{r_2}{\mathrm{r}_1} \\ & \frac{\sigma_1}{\sigma_2}=3 \end{aligned}\)
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