A sphere of radius R and charge Q is placed inside an imaginary sphere of radius `2R` whose centre coincides with the given sphere. The flux related to imaginary sphere is:

Options

A. `Q/in_(0)`
B. `Q/(2in_(0))`
C. `(4Q)/in_(0)`
D. `(2Q)/in_(0)`

Explanation

To solve the problem of finding the electric flux through an imaginary sphere of radius `2R` that encloses a sphere of radius `R` with charge `Q`, we can use Gauss's Law. Here’s the step-by-step solution:

### Step 1: Understand Gauss's Law
Gauss's Law states that the electric flux (Φ) through a closed surface is equal to the charge (Q_enc) enclosed by that surface divided by the permittivity of free space (ε₀). Mathematically, it is expressed as:

\[ \Phi = \frac{Q_{\text{enc}}}{\epsilon_0} \]

### Step 2: Identify the Charge Enclosed
In this scenario, we have a sphere of radius `R` with charge `Q` placed inside an imaginary sphere of radius `2R`. Since the charge `Q` is fully enclosed by the imaginary sphere, we can say that:

\[ Q_{\text{enc}} = Q \]

### Step 3: Apply Gauss's Law
Now, we can apply Gauss's Law to find the electric flux through the imaginary sphere of radius `2R`:

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

### Step 4: Conclusion
Thus, the electric flux related to the imaginary sphere is:

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

Now, we can check the options provided in the question to find the correct answer.

### Final Answer
The flux related to the imaginary sphere is:

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