Question

A cubical region of side a has its centre at the origin. It encloses three fixed point charges, $-q$ at $(0,-a/4,0),+3q$ at $(0,0,0)$ and $-q$ at $(0,+a/4,0)$. Choose the correct options(s)

• A. The net electric flux crossing the plane $x=+a/2$ is equal to the net electric flux crossing the plane $x=$ $-a/2$
• B. The net electric flux crossing the plane $y=+a/2$ is more than the net electric flux crossing the plane $y=$ $-a/2$
• C. The net electric flux crossing the entire region is $\frac{q}{{\epsilon }_0}$.
• D. The net electric flux crossing the plane $z=+a/2$ is equal to the net electric flux crossing the plane $x=$ $+a/2$

Answer 1

Answer: (A), (C), (D)

Net flux through the cubical region $=\frac{-q+3q-q}{{\epsilon }_0}=\frac{q}{{\epsilon }_0}$
The flux passing through the faces $x=\frac{-a}{2},x=+\frac{a}{2}$ and $z=+\frac{a}{2}$ are same due to symmetry.