Question

A point charge +q is placed precisely at the center of one of the faces of a perfectly symmetrical cube. What is the total electric flux passing through the cube?

• A. q/6\(\epsilon_0\)
• B. q/2\(\epsilon_0\)
• C. q/\(\epsilon_0\)
• D. q/3\(\epsilon_0\)

Hint:

Remember common symmetric charge placements for flux through a cube:
- Charge at center: \( q/\epsilon_0 \)
- Charge at center of a face: \( q/2\epsilon_0 \)
- Charge at midpoint of an edge: \( q/4\epsilon_0 \)
- Charge at a corner/vertex: \( q/8\epsilon_0 \)
These are derived by finding how many identical cubes are needed to symmetrically enclose the charge.

Answer 1

The Correct Option is B

Picture the field lines spreading out from the point charge equally in every direction, forming a complete sphere of radiating lines around it.

1. q/6\(\epsilon_0\): Would apply if the charge were at the cube's centre, sharing its flux equally among all six faces, which is not the case here.
2. q/2\(\epsilon_0\): Since the charge sits exactly on the plane of one face, that plane splits all the radiating field lines into two equal halves, one half going into the cube's interior and the other half escaping outward past that same face. Only the half going inward contributes to the cube's flux, giving \( \frac{1}{2}\times\frac{q}{\epsilon_0} = \frac{q}{2\epsilon_0} \).
3. q/\(\epsilon_0\): Would require all field lines to pass through the cube, which does not happen since half escape outward past the face the charge sits on.
4. q/3\(\epsilon_0\): Does not correspond to any natural half-space or symmetric division here.

Therefore, the correct answer is q/2\(\epsilon_0\).