Capacitance (in F) of a spherical conductor with radius 1m is

Options

A. `1.1xx10^(-10)`
B. `10^(-6)`
C. `9xx10^(-9)`
D. `10^(-3)`

Explanation

To find the capacitance of a spherical conductor with a radius of 1 meter, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Formula for Capacitance of a Sphere**:
The capacitance \( C \) of a spherical conductor is given by the formula:
\[ C = 4 \pi \epsilon_0 r \]
where:
- \( C \) is the capacitance,
- \( \epsilon_0 \) is the permittivity of free space (\( \epsilon_0 = 8.85 \times 10^{-12} \, \text{F/m} \)),
- \( r \) is the radius of the sphere.

2. **Substitute the Given Radius**:
In this case, the radius \( r \) is given as 1 meter. Therefore, we substitute \( r = 1 \, \text{m} \) into the formula:
\[ C = 4 \pi \epsilon_0 (1) \]

3. **Calculate the Capacitance**:
Now, we can calculate \( C \):
\[ C = 4 \pi (8.85 \times 10^{-12}) \]
\[ C = 4 \times 3.14 \times 8.85 \times 10^{-12} \]
\[ C \approx 1.11 \times 10^{-10} \, \text{F} \]

4. **Final Result**:
Therefore, the capacitance of the spherical conductor with a radius of 1 meter is:
\[ C \approx 1.11 \times 10^{-10} \, \text{F} \]

### Summary of the Solution:
The capacitance of a spherical conductor with a radius of 1 meter is approximately \( 1.11 \times 10^{-10} \, \text{F} \).