The charge on an originally uncharged insulated conductor is separated by induction from a positively charged rod brought near the conductor. For which of the various Gaussian surfaces represented by the dashed lines does electric flux = 0?

Question

The charge on an originally uncharged insulated conductor is separated by induction from a positively charged rod brought near the conductor. For which of the various Gaussian surfaces represented by the dashed lines does electric flux  = 0?

Quizplus · Accepted Answer

The electric flux through a Gaussian surface is given by the equation $Φ_E = q_{enclosed}/ε_0$, where $q_{enclosed}$ is the charge enclosed by the Gaussian surface and $ε_0$ is the permittivity of free space. Since the electric field lines are perpendicular to the Gaussian surfaces, the flux is proportional to the amount of charge enclosed by the surface.

In this problem, the charged rod induces a separation of charge in the insulated conductor. The side of the conductor closest to the rod becomes negatively charged while the side farthest from the rod becomes positively charged. The Gaussian surfaces SS1U1B11 to SS1U1B15 are all perpendicular to the surface of the conductor, and each encloses some fraction of the induced charges. We are looking for a Gaussian surface that encloses zero net charge so that the electric flux passing through it is zero.

The induced negative and positive charges in the conductor are equal in magnitude, so the sum of these will be zero. Only the Gaussian surface SS1U1B14 passes through the boundary between the negative and positive charges, which are equal and opposite. Thus, the net charge enclosed by this surface is zero, and the electric flux through it is zero. Therefore, the correct answer is D.

The Charge on an Originally Uncharged Insulated Conductor Is Separated