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AP EAMCET202018 Sep 2020Evening ShiftPhysicsCapacitanceActual

The capacitance of a spherical condenser is (1 F ). If the spacing between the two spheres is (1 ~mm ), the radius of the outer sphere is

Options

  1. A(30 ~cm )
  2. B(6 ~m )
  3. C(5 ~cm )
  4. D(3 ~m )

Correct answer

D. (3 ~m )

Step-by-step solution

Given, capacitance of spherical capacitor, (C=1 F =10⁻⁶ ~F ) Spacing between two spheres of spherical capacitor, (r₂-r₁=1 ~mm =10⁻³ ~m ) ( array ll & C=4 ₀ r₁ r₂ r₂-r₁ & 10⁻⁶= 1 9 10^9 (r₂-10⁻³ ) r₂ 10⁻³ & 9=r₂^2-10⁻³ r₂ 9000=1000 r₂^2-r₂ & 1000 r₂^2-r₂-9000=0 array ) ( aligned r₂ & = -(-1) (-1)^2-4 1000 (-9000) 2 1000 & = 1 36 10^6 2000 = 1 6000 2000 & = 1+6000 2000 =3.0005 3 ~m aligned )

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