An infinitely long uniform line charge distribution of charge per… - Vidyadip

MCQ

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

A
$4$
B
$5$
✓
$6$
D
$7$

✓

Answer

Correct option: C.

$6$

c
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 ' $n$ ' $=6$

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