Question

The capacitance of earth, viewed as a spherical conductor of radius 6408 km is: (a) 1420 μF
(b) 712 μF
(c) 680 μF
(d) 540 μF

Answer 1

(b) 712uF is the correct answer.

Answer 2

The capacitance of the earth is 712 μF hence, option (b) is correct choice.

We have to find the capacitance of the earth viewed as a spherical conductor of radius 6408 km.

We know, capacitance of a spherical conductor is given by, C = 4π∈₀r

where, ∈₀ is permittivity of vacuum and r is the radius of spherical conductor.

Here, r = 6408 km = 6.408 × 10⁶ m

∈₀ = 8.854 × 10⁻¹² m⁻³kg⁻¹s⁴A²

∴ C = 4 × 3.14 × 8.854 × 10⁻¹² × 6.408 × 10⁶ F

= 12.56 × 8.854 × 6.408 × 10⁻⁶ F

= 712.609 × 10⁻⁶ F ≈ 712 μF

Therefore the capacitance of the earth is 712 μF hence, option (b) is correct choice.