Question

The inward electric flux through a closed surface is \( 6 \times 10^{-5} \) and the outward flux is \( 3 \times 10^{-5} \). Then the total charge enclosed is?

• A. \( 9 \times 10^{-5} \, \text{C} \)
• B. \( 3 \times 10^{-5} \, \text{C} \)
• C. \( 6 \times 10^{-5} \, \text{C} \)
• D. \( 0 \, \text{C} \)

Hint:

Gauss's law states that the total charge enclosed by a surface is proportional to the net electric flux passing through the surface.

Answer 1

The Correct Option is A

According to Gauss's law, the total charge enclosed by a surface is proportional to the net electric flux through the surface. Mathematically, Gauss's law is expressed as: \[ \Phi_{\text{total}} = \frac{Q_{\text{enclosed}}}{\varepsilon_0} \] Where: - \( \Phi_{\text{total}} \) is the total electric flux, - \( Q_{\text{enclosed}} \) is the charge enclosed, - \( \varepsilon_0 \) is the permittivity of free space. The total flux is the sum of the inward and outward flux: \[ \Phi_{\text{total}} = 6 \times 10^{-5} - 3 \times 10^{-5} = 3 \times 10^{-5} \, \text{C} \] Thus, the total charge enclosed is: \[ Q_{\text{enclosed}} = 9 \times 10^{-5} \, \text{C} \]