An infinitely long uniform line charge distribution of charge per unit length λ lies parallel to y

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1. Electric Charges and Fields

medium

An infinitely long uniform line charge distribution of charge per unit length $\lambda$ lies parallel to the $y$-axis in the $y-z$ plane at $z=\frac{\sqrt{3}}{2} a$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $A B C D$ lying in the $x-y$ plane with its center at the origin is $\frac{\lambda L }{ n \varepsilon_0}\left(\varepsilon_0=\right.$ permittivity of free space $)$, then the value of $n$ is

$4$

$5$

$6$

$7$

(IIT-2015)

From the figure $\theta=60^{\circ}$

So No. of rectangular surfaces used to form a

$m =\frac{360}{60}=6$

So, $\phi=\frac{(\lambda L)}{6 \varepsilon_0}$, Hence ' $n$ ' $=6$

Standard 12

Physics

hard

(IIT-2011)

medium

(JEE MAIN-2015)

easy

hard

easy