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
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
- [AIEEE 2012]
- A
$\pi {a^2}E$
- B
$\frac{{\pi {a^2}E}}{{\sqrt 2 }}$
- C
$\frac{{\pi {a^2}E}}{{2\sqrt 2 }}$
- D
$\frac{{(\pi + 2)\,\pi {a^2}E}}{{{{(2\sqrt 2 )}^2}}}$
Similar Questions
If the electric flux entering and leaving an enclosed surface respectively is ${\varphi _1}$ and ${\varphi _2}$ the electric charge inside the surface will be
If the electric flux entering and leaving an enclosed surface respectively is ${\varphi _1}$ and ${\varphi _2}$ the electric charge inside the surface will be
- [AIEEE 2003]
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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Take $\left.\varepsilon_0=9 \times 10^{-12} C ^2 / Nm ^2\right)$
- [JEE MAIN 2023]
A square surface of side $L$ meter in the plane of the paper is placed in a uniform electric field $E(volt/m)$ acting along the same plane at an angle $\theta$ with the horizontal side of the square as shown in figure.The electric flux linked to the surface, in units of $volt \;m $
A square surface of side $L$ meter in the plane of the paper is placed in a uniform electric field $E(volt/m)$ acting along the same plane at an angle $\theta$ with the horizontal side of the square as shown in figure.The electric flux linked to the surface, in units of $volt \;m $
- [AIPMT 2010]
Is electric flux scalar or vector ?
Is electric flux scalar or vector ?
Consider a uniform electric field $E =3 \times 10^{3} i\; N / C .$
$(a)$ What is the flux of this field through a square of $10 \;cm$ on a side whose plane is parallel to the $y z$ plane?
$(b)$ What is the flux through the same square if the normal to its plane makes a $60^{\circ}$ angle with the $x -$axis?
Consider a uniform electric field $E =3 \times 10^{3} i\; N / C .$
$(a)$ What is the flux of this field through a square of $10 \;cm$ on a side whose plane is parallel to the $y z$ plane?
$(b)$ What is the flux through the same square if the normal to its plane makes a $60^{\circ}$ angle with the $x -$axis?