Question

A point charge is placed at the corner of a cube. The electric flux through the shaded surface is

• A. $\frac{q}{8{\epsilon }_0}$
• B. $\frac{q}{{\epsilon }_0}$
• C. $\frac{q}{24{\epsilon }_0}$
• D. $\frac{q}{12{\epsilon }_0}$

Answer 1

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

$\text{Step 1: Choosing gaussian surface}$

To calculate the electric flux through the shaded area, we have to make a Gaussian surface such that a given charge appears at the center of the bigger cube resulting from the combination of $8$ small cubes (as shown in figure)

$\text{Step 2: Flux through one cube}$

If a charge is at the corner then it is being shared by $8$ cubes.

Flux passing through the given cube will be $=\frac{q}{8{ϵ}_0}$

$\text{Step 3: Electric flux through shaded area}$

Now for any cube, it is touching $3$ of its faces. The area vector of that side and electric field vector will be perpendicular so flux through $3$ sides will be $0$.

An equal amount of flux will flow from other $3$ sides.

Flux through shaded area $=\frac{q}{8\times 3{\in }_0}$

$=\frac{q}{24{\in }_0}$

Hence, Option(C) is correct.