Question

Find the electric flux through one face of a cube if a charge \(q\) is placed at its center.

• A. \( \frac{q}{\epsilon_0} \)
• B. \( \frac{q}{2\epsilon_0} \)
• C. \( \frac{q}{6\epsilon_0} \)
• D. \( \frac{q}{12\epsilon_0} \)

Hint:

Think about the solid angle a face subtends at the charge, rather than dividing the total flux directly. Since the charge is at the centre, all six faces of the cube are equally placed around it, so the total solid angle around the charge splits equally among them.

Answer 1

The Correct Option is C

Topic: Electrostatics (Gauss's Law)
Step 1: Understanding the Question:
A point charge is placed at the center of a cube. We need to find the electric flux passing through only one of the six faces of the cube.
Step 2: Key Formula or Approach:
According to Gauss's Law, the total electric flux (\(\Phi_{total}\)) through any closed surface enclosing a charge \(q\) is:
\[ \Phi_{total} = \frac{q}{\epsilon_0} \]
Step 3: Detailed Explanation:
A cube is a symmetric closed surface consisting of 6 identical square faces.
When the charge is placed exactly at the center, the electric field lines are distributed uniformly in all directions.
By symmetry, the total flux will be divided equally among all 6 faces.
\[ \Phi_{one \ face} = \frac{\Phi_{total}}{6} \]
\[ \Phi_{one \ face} = \frac{q}{6\epsilon_0} \]
Step 4: Final Answer:
The electric flux through one face is \(\frac{q}{6\epsilon_0}\).