Volume charge density of a sphere of radius 6 ,m is 2 ,μ cm ^{-3} . number of lines of force per un

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1. Electric Charges and Fields

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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 $\left.\epsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1}- m ^{-2}\right]$

A

$44$

B

$43$

C

$45$

D

$42$

(JEE MAIN-2022)

Solution

No. of electric field lines per unit area $=$ electric field.

$E =\frac{\rho r}{3 \epsilon_{0}}, \text { for } r=R$

$E=\frac{\rho R}{3 \epsilon_{0}}=\frac{2 \times 6}{3 \times 8.85 \times 10^{-12}}=0.45 \times 10^{12}\,NC ^{-1}$

$=45 \times 10^{10}\,N / C$

Standard 12

Physics

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