Question

A charge Q µc is placed at the centre of cube, the flux coming out from any surfaces will be : -

• A. \(\frac{Q}{6\epsilon_0}\times 10^{-6}\)
• B. \(\frac{Q}{6\epsilon_0}\times 10^{-3}\)
• C. \(\frac{Q}{2\epsilon_0}\)
• D. \(\frac{Q}{8\epsilon_0}\)

Answer 1

The Correct Option is A

To solve this problem, we need to understand the concept of electric flux and how it relates to a charge placed inside a closed surface like a cube.

Gauss's Law: According to Gauss's law, the total electric flux \(\Phi\) through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of the medium (\(\epsilon_0\) for free space).

The formula for Gauss's law is:

\[\Phi = \frac{Q}{\epsilon_0}\]

Here:

• Q is the charge enclosed, which is given as Q \, \mu c (microcoulombs).
• \(\epsilon_0\) is the permittivity of free space.

When a charge is placed at the center of a symmetrical shape like a cube, it is uniformly enclosed by the cube. The entire flux \(\frac{Q}{\epsilon_0}\) is uniformly distributed across all six faces of the cube.

Flux through One Face: Since the charge is symmetrically centered, the flux through each of the six faces of the cube will be equal. Therefore, flux through one face is:

\[\Phi_{\text{one face}} = \frac{Q}{6\epsilon_0}\]

Since the charge is given in microcoulombs, we need to convert it to coulombs by multiplying by 10^{-6}. Thus, the flux through one face becomes:

\[\Phi_{\text{one face}} = \frac{Q}{6\epsilon_0} \times 10^{-6}\]

Therefore, the correct answer is:

Option A: \(\frac{Q}{6\epsilon_0}\times 10^{-6}\)