Question

A charge 'Q' C is placed at the centre of a cube. The electric flux through two opposite faces of the cube is
(\(ε_0\) = permittivity of free space)

• A. \(\frac{Q}{6ε_0}\)
• B. \(\frac{Q}{3ε_0}\)
• C. \(\frac{Q}{ε_0}\)
• D. \(\frac{Q}{2ε_0}\)

Hint:

Gauss law gives the total flux Q over epsilon naught, and symmetry splits it equally over the six faces.

Answer 1

The Correct Option is B

Step 1: Use symmetry.
The six faces are equivalent, so each takes one sixth of the total flux.

Step 2: Fraction.
Two faces take $2/6 = 1/3$ of the total flux.

Step 3: Result.
$\dfrac{1}{3}\times\dfrac{Q}{\varepsilon_0} = \dfrac{Q}{3\varepsilon_0}$.

Final Answer:
Option (B). \[ \boxed{\frac{Q}{3\varepsilon_0}} \]