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
$\frac{{15}}{2}\frac{q}{{{\varepsilon _0}}}$
- B
$\frac{{4q}}{{{\varepsilon _0}}}$
- C
$\frac{q}{{{\varepsilon _0}}}$
- D
$\frac{{2q}}{{{\varepsilon _0}}}$
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An electric field converges at the origin whose magnitude is given by the expression $E = 100\,r\,Nt/Coul$, where $r$ is the distance measured from the origin.
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The electric field in a region is given $\overrightarrow{ E }=\left(\frac{3}{5} E _{0} \hat{ i }+\frac{4}{5} E _{0} \hat{ j }\right) \frac{ N }{ C } .$ The ratio of flux of reported field through the rectangular surface of area $0.2\, m ^{2}$ (parallel to $y - z$ plane) to that of the surface of area $0.3\, m ^{2}$ (parallel to $x - z$ plane $)$ is $a : b ,$ where $a =$ .............
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[Here $\hat{ i }, \hat{ j }$ and $\hat{ k }$ are unit vectors along $x , y$ and $z-$axes respectively]
- [JEE MAIN 2021]
Is electric flux scalar or vector ?
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As shown in figure, a cuboid lies in a region with electric field $E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} \quad N / C$. The magnitude of charge within the cuboid is $n \varepsilon_0 C$. The value of $n$ is $............$ (if dimension of cuboid is $1 \times 2 \times 3 \;m ^3$ )
As shown in figure, a cuboid lies in a region with electric field $E=2 x^2 \hat{i}-4 y \hat{j}+6 \hat{k} \quad N / C$. The magnitude of charge within the cuboid is $n \varepsilon_0 C$. The value of $n$ is $............$ (if dimension of cuboid is $1 \times 2 \times 3 \;m ^3$ )
- [JEE MAIN 2023]