Surface subtends a solid angle of `pi` on a point charge +q. Electric flux due to point charge, associated with the given surface, is

Options

A. `q//epsilon_0`
B. `q//2epsilon_0`
C. `q//4epsilon_0`
D. `q//8epsilon_0`

Explanation

To solve the problem of finding the electric flux due to a point charge \( +q \) associated with a surface that subtends a solid angle of \( \pi \), we can follow these steps:

### Step 1: Understand the Concept of Electric Flux
Electric flux (\( \Phi \)) through a surface is defined as the product of the electric field (\( E \)) and the area (\( A \)) of the surface projected in the direction of the field. Mathematically, it is given by:
\[ \Phi = \int \vec{E} \cdot d\vec{A} \]
For a point charge, we can also use Gauss's law, which states:
\[ \Phi = \frac{q_{\text{enc}}}{\epsilon_0} \]
where \( q_{\text{enc}} \) is the charge enclosed by the surface and \( \epsilon_0 \) is the permittivity of free space.

### Step 2: Determine the Total Electric Flux for a Complete Sphere
When a point charge \( +q \) is enclosed by a surface (like a sphere), the total electric flux through that surface is:
\[ \Phi_{\text{total}} = \frac{q}{\epsilon_0} \]
This total flux corresponds to a solid angle of \( 4\pi \) steradians, which is the solid angle for a complete sphere.

### Step 3: Relate Solid Angle to Electric Flux
The total solid angle around a point charge is \( 4\pi \) steradians. Since the surface in question subtends a solid angle of \( \pi \) steradians, we can find the fraction of the total flux that corresponds to this solid angle.

### Step 4: Calculate the Electric Flux for the Given Solid Angle
The electric flux associated with the solid angle \( \pi \) can be calculated as:
\[ \Phi = \frac{\text{Solid Angle}}{4\pi} \times \Phi_{\text{total}} \]
Substituting the values we have:
\[ \Phi = \frac{\pi}{4\pi} \times \frac{q}{\epsilon_0} = \frac{1}{4} \times \frac{q}{\epsilon_0} = \frac{q}{4\epsilon_0} \]

### Final Answer
Thus, the electric flux due to the point charge \( +q \) associated with the given surface that subtends a solid angle of \( \pi \) is:
\[ \Phi = \frac{q}{4\epsilon_0} \]