If a spherical conductor comes out from the closed surface of the sphere then total flux emitted from the surface will be

  • A

    $\frac{1}{{{\varepsilon _0}}} \times $ (the charge enclosed by surface)

  • B

    ${\varepsilon _0} \times $ (charge enclosed by surface)

  • C

    $\frac{1}{{4\pi {\varepsilon _0}}} \times $ (charge enclosed by surface)

  • D

    $0$

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A cubical volume is bounded by the surfaces $x =0, x = a , y =0, y = a , z =0, z = a$. The electric field in the region is given by $\overrightarrow{ E }= E _0 \times \hat{ i }$. Where $E _0=4 \times 10^4 NC ^{-1} m ^{-1}$. If $a =2 cm$, the charge contained in the cubical volume is $Q \times 10^{-14} C$. The value of $Q$ is $...........$

Take $\left.\varepsilon_0=9 \times 10^{-12} C ^2 / Nm ^2\right)$ 

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The flat base of a hemisphere of radius $a$ with no charge inside it lies in a horizontal plane. A uniform electric field $\vec E$ is applied at an angle $\frac {\pi }{4}$ with the vertical direction. The electric flux through the curved surface of the hemisphere is

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