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  4. The volume charge density of a sphere of radius 6 m is 2 μ 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 C 2 N -1- m -2]

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

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Solution:

No. of electric field lines per unit area $=$ electric field.
$E =\frac{\rho r }{3 \in_0}$, for $r = R$
$E =\frac{\rho R }{3 \epsilon_0}=\frac{2 \times 6}{3 \times 8.85 \times 10^{-12}}=0.45 \times 10^{12} NC ^{-1}$
$=45 \times 10^{10} N / C$