The total flux ( in S.I units ) through a closed surface constructed around a positive charge of 0.5 C placed in a dielectric medium of dielectric constant 10 is

Options

A. `5.65xx10^9`
B. `1.13xx10^(11)`
C. `9xx10^9`
D. `8.85xx10^(-12)`

Answer

To find the total electric flux through a closed surface surrounding a positive charge of 0.5 C placed in a dielectric medium with a dielectric constant of 10, we can use Gauss's law.

### Step-by-Step Solution:

1. **Understand Gauss's Law**:
Gauss's law states that the electric flux (Φ) through a closed surface is equal to the charge enclosed (Q) divided by the permittivity of the medium (ε). Mathematically, it is expressed as:
\[ \Phi = \frac{Q}{\epsilon} \]

2. **Identify the Charge and Dielectric Constant**:
We are given:
- Charge, \( Q = 0.5 \, \text{C} \)
- Dielectric constant, \( k = 10 \)

3. **Calculate the Permittivity**:
The permittivity (ε) of the medium can be expressed as:
\[ \epsilon = \epsilon_0 \cdot k \]
where \( \epsilon_0 \) (the permittivity of free space) is approximately \( 8.85 \times 10^{-12} \, \text{F/m} \).

Therefore, we calculate:
\[ \epsilon = 8.85 \times 10^{-12} \, \text{F/m} \times 10 = 8.85 \times 10^{-11} \, \text{F/m} \]

4. **Substitute Values into Gauss's Law**:
Now we can substitute the values into Gauss's law:
\[ \Phi = \frac{Q}{\epsilon} = \frac{0.5 \, \text{C}}{8.85 \times 10^{-11} \, \text{F/m}} \]

5. **Calculate the Electric Flux**:
Performing the calculation:
\[ \Phi = \frac{0.5}{8.85 \times 10^{-11}} \approx 5.65 \times 10^{9} \, \text{N m}^2/\text{C} \]

6. **Final Result**:
The total flux through the closed surface is:
\[ \Phi \approx 5.65 \times 10^{9} \, \text{N m}^2/\text{C} \]