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JEE Main 2022 (25 Jul, Shift 2) · Capacitance of a Conductor

Capacitance of a Conductor question from JEE Main 2022 (25 Jul, Shift 2)

Q12JEE Main 2022 · 25 JUL · SHIFT 2Medium

Capacitance of a Conductor

Capacitance of an isolated conducting sphere of radius R1 becomes n times when it is enclosed by a concentric conducting sphere of radius R2 connected to earth. The ratio of their radii (R2R1)\left(\frac{R_2}{R_1}\right) is:

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Answer: (a)

  1. Isolated sphere: C=4πε0R1C = 4\pi\varepsilon_0 R_1.
  2. With earthed outer shell (spherical capacitor): C′=4πε0R1R2R2−R1C' = \frac{4\pi\varepsilon_0 R_1R_2}{R_2 - R_1}.
  3. C′=nC⇒R2R2−R1=n⇒R2(n−1)=nR1C' = nC \Rightarrow \frac{R_2}{R_2 - R_1} = n \Rightarrow R_2(n-1) = nR_1
  4. So the answer is (a) R2R1=nn−1\frac{R_2}{R_1} = \frac{n}{n-1}.
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