Question

If charge $q$ is placed on one of the vertex of a cube, then total electric flux passing through the cube is ______.

• A. $\frac{q}{\varepsilon_0}$
• B. $\frac{q}{8\varepsilon_0}$
• C. $\frac{q}{4\varepsilon_0}$
• D. $\frac{q}{24\varepsilon_0}$

Hint:

If the question asks for the flux through a specific \textbf{face} of that cube (not adjacent to the vertex), the answer would be $q/24\varepsilon_0$ because only 3 faces of the cube are "hit" by the field lines.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
According to Gauss's Law, the total electric flux through a closed surface is $1/\varepsilon_0$ times the net charge enclosed. If a charge is not fully enclosed, we must imagine a symmetrical structure to enclose it.
Step 2: Detailed Explanation:
A charge placed at the corner (vertex) of a cube is shared by 8 identical cubes meeting at that point. To fully enclose the charge $q$ symmetrically, we need a larger "super-cube" made of 8 smaller cubes. The total flux through this large cube is $q/\varepsilon_0$. Since the flux is distributed equally among the 8 cubes, the flux through one single cube is: $$\Phi = \frac{1}{8} \left( \frac{q}{\varepsilon_0} \right)$$
Step 3: Final Answer:
The correct option is (b).