Question

The electric flux $\varphi$ through a hemispherical surface of radius R, placed in a uniform electric field of intensity E parallel to the axis of its circular plane is :

• A. $\left(4/3\right)\pi R^{3}E$
• B. $2\pi R^{2}E$
• C. $\pi R^{2}E$
• D. $2\pi RE$

Answer 1

Answer: (C)

$\pi R^{2}E$

As the field intensity E is parallel to axis of circular plane so only this circular surface will contribute the flux through the hemisphere.
By Gauss's law, flux , $\varphi =\int E.ds=E.\pi R^2$