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Capacitor question

2002 · Shift 0 · Q140
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Capacitor question

2002 · Shift 0 · Q140

JEE MainPhysicsCapacitorMCQ+4 / −1
Capacitance (in FFF) of a spherical conductor with radius 1m1m1m is
  1. A
    1.1×10−101.1 \times {10^{ - 10}}1.1×10−10
  2. B
    10−6{10^{ - 6}}10−6
  3. C
    9×10−99 \times {10^{ - 9}}9×10−9
  4. D
    10−3{10^{ - 3}}10−3
View written solutionFree

Correct answer: A

  1. Capacitance of an isolated spherical conductor

    For an isolated spherical conductor of radius RRR, the capacitance is C=4πε0RC = 4\pi \varepsilon_0 RC=4πε0​R

  2. Given data

    Radius: R=1 mR = 1\,\text{m}R=1m

    Permittivity of free space: ε0=8.85×10−12 F/m\varepsilon_0 = 8.85 \times 10^{-12}\,\text{F/m}ε0​=8.85×10−12F/m

  3. Substitute the values

    C=4π(8.85×10−12)(1)C = 4\pi (8.85 \times 10^{-12})(1)C=4π(8.85×10−12)(1)

  4. Calculate

    Since 4π≈12.574\pi \approx 12.574π≈12.57

    therefore, C≈12.57×8.85×10−12C \approx 12.57 \times 8.85 \times 10^{-12}C≈12.57×8.85×10−12

    C≈111.3×10−12C \approx 111.3 \times 10^{-12}C≈111.3×10−12

    C≈1.11×10−10 FC \approx 1.11 \times 10^{-10}\,\text{F}C≈1.11×10−10F

  5. Match with options

    1.11×10−10 F≈1.1×10−10 F1.11 \times 10^{-10}\,\text{F} \approx 1.1 \times 10^{-10}\,\text{F}1.11×10−10F≈1.1×10−10F

    This corresponds to Option A.

  6. Comparison with stored correct answer

    Stored correct answer: A

    Derived answer: A

    Hence, they agree.

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