A charge of 8.85C is placed at the centre of a spherical Guassian surface of radius 5cm. The electric flux through the surface is

Options

A. `10^(12)V//m`
B. `10^(-12) V//m`
C. `10^(8) V//m`
D. `10^(10)V//m`

Answer

To find the electric flux through a spherical Gaussian surface surrounding a charge, we can use Gauss's Law. Here’s how to solve the problem step by step:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Charge (Q) = 8.85 C
- Radius of the Gaussian surface (r) = 5 cm (this value is not directly needed for the calculation of electric flux)

2. **Understand Gauss's Law:**
Gauss's Law states that the electric flux (Φ) through a closed surface is proportional to the charge enclosed (Q) by that surface. Mathematically, it is expressed as:
\[ \Phi = \frac{Q}{\epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space.

3. **Use the Value of Permittivity:**
The permittivity of free space (\( \epsilon_0 \)) is approximately:
\[ \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \]

4. **Calculate the Electric Flux:**
Substitute the values into Gauss's Law:
\[ \Phi = \frac{8.85 \, \text{C}}{8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2} \]
Simplifying this gives:
\[ \Phi = 1 \times 10^{12} \, \text{N m}^2/\text{C} \]
Since \( 1 \, \text{N m}^2/\text{C} = 1 \, \text{V m} \), we can express the flux as:
\[ \Phi = 10^{12} \, \text{V m} \]

5. **Conclusion:**
The electric flux through the surface is:
\[ \Phi = 10^{12} \, \text{V m} \]

### Final Answer:
The electric flux through the surface is \( 10^{12} \, \text{V m} \).

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