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1. Electric Charges and Fields
medium
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
A
$\pi {a^2}E$
B
$\frac{{\pi {a^2}E}}{{\sqrt 2 }}$
C
$\frac{{\pi {a^2}E}}{{2\sqrt 2 }}$
D
$\frac{{(\pi + 2)\,\pi {a^2}E}}{{{{(2\sqrt 2 )}^2}}}$
(AIEEE-2012)
Solution
We know that.
$\phi=\oint E d S=E \oint d S \cos 45^{\circ}$
In case of hemisphere
$\phi_{\text {curved }}=\dot{\phi}_{\text {cirrular }}$
Therefore. $\phi_{\text {curved }}=E \pi a^{2} \cdot \frac{1}{\sqrt{2}}=\frac{E \pi a^{2}}{\sqrt{2}}$
Standard 12
Physics
