Question

A closed surface encloses \(n\) electric dipoles. The net electric flux through the closed surface is
(\(\epsilon _{0}\) = permittivity of free space, q = charge)

• A. \(\frac{nq}{\epsilon _{0}}\)
• B. \(n\epsilon _{0}q\)
• C. \(\frac{q}{\epsilon _{0}}\)
• D. \(0\)

Hint:

A dipole has zero net charge, so the enclosed charge and the flux are zero.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
Gauss's law states \(\phi=\dfrac{q_{enc}}{\epsilon_0}\), where \(q_{enc}\) is the net charge enclosed.

Step 2: Charge of a dipole
Each dipole consists of charges \(+q\) and \(-q\), so its net charge is zero.

Step 3: Calculation
With \(n\) dipoles inside, \(q_{enc}=n(q-q)=0\).
So \(\phi=\dfrac{0}{\epsilon_0}=0\).

Final Answer:
The net flux through the closed surface is zero. \[ \boxed{\text{(D) }0} \]