Question

You are given a dipole of charge \( +q \) and \( -q \) separated by a distance \( 2l \). A sphere 'A' of radius \( R \) passes through the centre of the dipole as shown below and another sphere 'B' of radius \( 2R \) passes through the charge \( +q \). Then the electric flux through the sphere A is 

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

Hint:

When dealing with electric flux through a closed surface, the flux depends on the net charge enclosed. For a dipole, the net charge is zero, so the flux is also zero.

Answer 1

The Correct Option is D

The electric flux through any closed surface is given by Gauss's Law: \[ \Phi = \frac{Q_{\text{enc}}}{\epsilon_0} \] where \( Q_{\text{enc}} \) is the charge enclosed by the Gaussian surface and \( \epsilon_0 \) is the permittivity of free space. - For sphere A, the dipole is positioned in such a way that it passes through the centre of the dipole. The total charge enclosed by sphere A is zero, because the dipole consists of two equal and opposite charges \( +q \) and \( -q \). - Therefore, the net charge enclosed by the surface of sphere A is zero. Hence, the electric flux through sphere A is: \[ \Phi = \frac{0}{\epsilon_0} = 0 \] Thus, the correct answer is: \[ \text{Zero} \]