The volume charge density of a sphere of radius 6 m is 2 cm⁻³. The number of lines of force per unit surface area coming out from the surface of the sphere is _______________ × 10¹⁰ NC⁻¹. [Given: Permittivity of vacuum ε₀ = 8.85 × 10⁻¹² C² N⁻¹-m⁻² ] Numerical answer type. Work it out, then open the answer.

Answer: 45. Lines of force per unit area = field at the surface, E = (ρ R)/(3ε₀). ρ = 2 μ C cm ⁻³ = 2 C m ⁻³, R = 6 m. E = 2 × 63 × 8.85 × 10⁻¹² = 4.52 × 10¹¹ ≈ 45 × 10¹⁰ N C ⁻¹ So the answer is 45.

The volume charge density of a sphere of radius 6 m is 2 cm⁻³. The… | JEE Main 2022 (25 Jul, Shift 1)

Q77JEE Main 2022 · 25 JUL · SHIFT 1Medium

Electric Flux & Gauss's Law

The volume charge density of a sphere of radius $6\text{ m}$ is $2\ \mu\text{C cm}^{-3}$ . The number of lines of force per unit surface area coming out from the surface of the sphere is _______________ $\times 10^{10}\text{ NC}^{-1}$ . [Given: Permittivity of vacuum $\epsilon_0 = 8.85 \times 10^{-12}\text{ C}^{2}\text{ N}^{-1}\text{-m}^{-2}$ ]

Numerical answer type. Work it out, then open the answer.

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Answer: 45

Lines of force per unit area = field at the surface, $E = \frac{\rho R}{3\varepsilon_0}$ .
$\rho = 2\ \mu$ C cm $^{-3}$ $= 2$ C m $^{-3}$ , $R = 6$ m.
$E = \frac{2 \times 6}{3 \times 8.85 \times 10^{-12}} = 4.52 \times 10^{11} \approx 45 \times 10^{10}$ N C $^{-1}$
So the answer is 45.

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