Question

The total electric flux through a closed spherical surface of radius ‘r’ enclosing an electric dipole of dipole moment 2aq is (Give ε₀ = permittivity of free space)

• A. Zero
• B. \(\frac{q}{\epsilon_0}\)
• C. \(\frac{2q}{\epsilon_0}\)
• D. \(\frac{8\pi r^2q}{\epsilon_0}\)

Answer 1

The Correct Option is A

The given question is about the electric flux through a closed spherical surface enclosing an electric dipole.

Step 1: Apply Gauss's Law

The electric flux \( \Phi_E \) is given by Gauss's law:

\[ \Phi_E = \frac{q_{\text{enclosed}}}{\epsilon_0} \]

Step 2: Understanding the Dipole

A dipole consists of two equal and opposite charges, so the total charge enclosed by the spherical surface is zero. Thus, the flux is zero:

\[ \Phi_E = 0 \]

The correct answer is (A) Zero.

Answer 2

The electric flux through a closed surface is given by Gauss's Law: \[ \Phi = \frac{Q_{\text{enclosed}}}{\varepsilon_0} \] For a dipole, the total enclosed charge is zero, as the positive and negative charges cancel each other out. Therefore, the electric flux through the spherical surface enclosing the dipole is zero.

Thus, the correct answer is Zero.