The volume charge density of a sphere of radius $6 m$ is $2 μC {cm}^{- 3}$ . The number of lines of force per unit surface area coming out from the surface of the sphere is _____ $\times 10^{10} N C^{- 1} .$
[Given : Permittivity of vacuum $ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} - m^{- 2}$ ]

Question

The volume charge density of a sphere of radius $6 m$ is $2 μC {cm}^{- 3}$ . The number of lines of force per unit surface area coming out from the surface of the sphere is _____ $\times 10^{10} N C^{- 1} .$

[Given : Permittivity of vacuum $ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} - m^{- 2}$ ]

TestHub · Accepted Answer

Given here, ρ = 2 μC cm - 3 and R = 6 m . Number of lines of force per unit area = electric field at surface = K Q R 2 E = 1 4 π ε 0 ρ 4 3 π R 3 R 2 E = ρ R 3 ϵ 0 = 2 × 6 3 × 8 . 85 × 10 - 12 = 0 . 45 × 10 12 N C - 1 = 45 × 10 10 N C - 1

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