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:

If a charge is placed at the center of a symmetric closed surface (like a cube), the total flux \( \frac{q}{\epsilon_0} \) distributes equally among all identical faces.

Answer 1

The Correct Option is C

Concept: According to Gauss's Law, the total electric flux through a closed surface is given by: \[ \Phi_{\text{total}} = \frac{q}{\epsilon_0} \] If a charge is placed at the center of a cube, the flux distributes equally among its six identical faces.

Step 1: Write the total flux through the cube. \[ \Phi_{\text{total}} = \frac{q}{\epsilon_0} \]

Step 2: Divide the flux equally among the six faces. \[ \Phi_{\text{one face}} = \frac{1}{6} \times \frac{q}{\epsilon_0} \] \[ \Phi_{\text{one face}} = \frac{q}{6\epsilon_0} \] Thus, the electric flux through one face is: \[ \boxed{\frac{q}{6\epsilon_0}} \]