An electric charge of `8.85 xx 10^(-13)C` is placed at the centre of a sphere of radius 1 m. The electric flux through the sphere is

Options

A. `0.2 N C^(-1) m^(2)`
B. `0.1 NC^(-1) m^(2)`
C. `0.3 NC^(-1) m^(2)`
D. `0.01 NC^(-1) m^(2)`

Explanation

To solve the problem of finding the electric flux through a sphere with a charge placed at its center, we can use Gauss's Law. Here’s a 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) enclosed by that surface divided by the permittivity of free space (ε₀):
\[ \Phi = \frac{Q_{\text{enclosed}}}{\epsilon_0} \]

### Step 2: Identify the Given Values
From the problem, we have:
- Charge \( Q = 8.85 \times 10^{-13} \, \text{C} \)
- The permittivity of free space \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \, \text{N}^{-1} \, \text{m}^{-2} \)

### Step 3: Substitute the Values into Gauss's Law
Now we can substitute the values into Gauss's Law:
\[ \Phi = \frac{8.85 \times 10^{-13}}{8.85 \times 10^{-12}} \]

### Step 4: Simplify the Expression
When we simplify the expression, we can cancel out \( 8.85 \) from the numerator and denominator:
\[ \Phi = \frac{1}{10} = 0.1 \, \text{N m}^2/\text{C} \]

### Step 5: Write the Final Answer
Thus, the electric flux through the sphere is:
\[ \Phi = 0.1 \, \text{N m}^2/\text{C} \]

### Conclusion
The electric flux through the sphere is \( 0.1 \, \text{N m}^2/\text{C} \).

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