Question

If charges $q/2$ and $2q$ are placed at the centre of face and at the corner of a cube, then the total flux through the cube will be:

• A. $\frac{q}{2{\epsilon }_0}$
• B. $\frac{q}{{\epsilon }_0}$
• C. $\frac{q}{6{\epsilon }_0}$
• D. $\frac{q}{8{\epsilon }_0}$

Answer 1

Answer: (A)

$\frac{q}{2{\epsilon }_0}$

$\text{Definition}:\text{When q is placed at any place in a closed surface}$

$\text{Flux is calculated only by the part of charge q inside the surface}$

Here,

In charge $2q$ only ${\frac{1}{8}}^{th}$ part is inside the cube,

And in charge $\frac{q}{2}$ only $\frac{1}{2}$ part is inside the cube.

So total flux $=\frac{\frac{q}{4}+\frac{q}{4}}{{\epsilon }_0}=\frac{q}{2{\epsilon }_0}$

Option $\text{A}$ is the correct answer.