Question

A flat, square surface with sides of length $L$ is described by the equations $x=L,0\le y\le L,0\le z\le L$
The electric flux through the square due to a positive point charge $q$ located at the origin $(x=0,y=0,z=0)$ is:

• A. $\frac{q}{4{ϵ}_0}$
• B. $\frac{q}{6{ϵ}_0}$
• C. $\frac{q}{24{ϵ}_0}$
• D. $\frac{q}{48{ϵ}_0}$

Answer 1

The correct option is C $\frac{q}{24{ϵ}_0}$


Total flux linked with the cube shown in figure due to charge placed at its corner
$=\left(\frac{q}{8{ϵ}_0}\right)$
(one-eighth part of the cube with centre at origin)

Now, this total flux passes through only 3 faces of the cube.
Hence, flux passing through square regionin question
${\varphi }^{\prime }=\frac{\left(\frac{q}{8{ϵ}_0}\right)}{3}=\frac{q}{24{ϵ}_0}$