Question

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. $\frac{\left(\pi+2\,\pi a^{2}\right)E}{\left(2\sqrt{2}\right)^2}$

Answer 1

Answer: (B)

We know that,
$\phi=\oint E.dS=E\oint dS\,cos 45^{°}$
In case of hemisphere
$\phi_{curved}=\phi _{circuler}$
Therefore, $\phi _{curved}=E\pi a^{2}. \frac{1}{\sqrt{2}}=\frac{E\,\pi a^{2}}{\sqrt{2}}$