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
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
- [IIT 2015]
- A
$4$
- B
$5$
- C
$6$
- D
$7$
Similar Questions
Figure shows electric field lines due to a charge configuration, from this we conclude that
Figure shows electric field lines due to a charge configuration, from this we conclude that
Draw electric field by negative charge.
Draw electric field by negative charge.
The figure shows a hollow hemisphere of radius $R$ in which two charges $3q$ and $5q$ are placed symmetrically about the centre $O$ on the planar surface. The electric flux over the curved surface is
The figure shows a hollow hemisphere of radius $R$ in which two charges $3q$ and $5q$ are placed symmetrically about the centre $O$ on the planar surface. The electric flux over the curved surface is
A point charge causes an electric flux of $-1.0 \times 10^{3}\; N\;m ^{2} / C$ to pass through a spherical Gaussian surface of $10.0\; cm$ radius centred on the charge.
$(a)$ If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?
$(b)$ What is the value of the point charge?
A point charge causes an electric flux of $-1.0 \times 10^{3}\; N\;m ^{2} / C$ to pass through a spherical Gaussian surface of $10.0\; cm$ radius centred on the charge.
$(a)$ If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?
$(b)$ What is the value of the point charge?
If the electric field is given by $(5 \hat{i}+4 \hat{j}+9 \hat{k})$. The electric flux through a surface of area $20$ units lying in the $Y-Z$ plane will be (in units)
If the electric field is given by $(5 \hat{i}+4 \hat{j}+9 \hat{k})$. The electric flux through a surface of area $20$ units lying in the $Y-Z$ plane will be (in units)
- [AIIMS 2019]