Question

The total electric flux coming out from stationary unit positive charge in air is

• A. \(\epsilon_0\)
• B. \((\epsilon_0)^{-1}\)
• C. 4\(\pi\epsilon_0\)
• D. \((4\pi\epsilon_0)^{-1}\)

Hint:

Gauss's Law is a powerful tool for calculating electric flux. Remember that the flux depends only on the enclosed charge, not on the shape or size of the Gaussian surface. For a point charge, the flux is the same through a small sphere around it as it is through a large, irregularly shaped surface enclosing it.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question requires the application of Gauss's Law in electrostatics. Gauss's Law relates the total electric flux (\(\Phi_E\)) through any closed surface (called a Gaussian surface) to the net electric charge (\(Q_{enc}\)) enclosed by that surface.
Step 2: Key Formula or Approach:
Gauss's Law is stated mathematically as:
\[ \Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\epsilon} \] Where:
\(\Phi_E\) is the total electric flux.
\(Q_{enc}\) is the total charge enclosed within the surface.
\(\epsilon\) is the permittivity of the medium. For air or vacuum, we use the permittivity of free space, \(\epsilon_0\).
Step 3: Detailed Explanation:
According to the problem statement:
- The charge is a "unit positive charge", which means \(Q_{enc} = +1\) C.
- The medium is "air", so we use the permittivity \(\epsilon_0\).
Substituting these values into Gauss's Law:
\[ \Phi_E = \frac{+1}{\epsilon_0} \] This can be written using a negative exponent as:
\[ \Phi_E = (\epsilon_0)^{-1} \] Step 4: Final Answer:
The total electric flux is \((\epsilon_0)^{-1}\). This corresponds to option (B).