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JEE Main 20258 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
8 April
Shift
Evening Shift
Subject
Physics
Chapter
Electrostatics

JEE Main 2025 · 8 April · Evening Shift · Physics · Electrostatics

Two metal spheres of radius R and 3 R have same surface charge...

Two metal spheres of radius RR and 3R3 R have same surface charge density σ\sigma. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ1\sigma_1 and σ2\sigma_2, respectively. The ratio σ1σ2\frac{\sigma_1}{\sigma_2} is.

Options

  1. A19\frac{1}{9}
  2. B9
  3. C13\frac{1}{3}
  4. D3

Correct answer

D. 3

Step-by-step solution

For conducting sphere, V=σrε0\mathrm{V}=\frac{\sigma \mathrm{r}}{\varepsilon_0}
After contact, V1=V2\mathrm{V}_1=\mathrm{V}_2
<br/>σ1r1=σ2r2σ1σ2=r2r1σ1σ2=3<br/>\begin{aligned}<br/>& \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<br/>\end{aligned}
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