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

Options

A. (a) `1.1xx10^-10`
B. (b) `10^-6`
C. (c) `9xx10^-9`
D. (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. **Understand the Formula for Capacitance of a Spherical Conductor:**
The capacitance \( C \) of an isolated 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 (\( \epsilon_0 \approx 8.85 \times 10^{-12} \, \text{F/m} \)),
- \( R \) is the radius of the sphere.

2. **Substitute the Given Values:**
We are given that the radius \( R = 1 \, \text{m} \). Therefore, we can substitute this value into the formula:
\[ C = 4 \pi \epsilon_0 \times 1 \]

3. **Calculate \( 4 \pi \epsilon_0 \):**
First, calculate \( 4 \pi \):
\[ 4 \pi \approx 12.5664 \]
Now, multiply this by \( \epsilon_0 \):
\[ C = 12.5664 \times 8.85 \times 10^{-12} \, \text{F} \]

4. **Perform the Multiplication:**
Now, calculate the product:
\[ C \approx 12.5664 \times 8.85 \times 10^{-12} \approx 1.11265 \times 10^{-10} \, \text{F} \]

5. **Round the Result:**
Rounding to two significant figures, we find:
\[ C \approx 1.1 \times 10^{-10} \, \text{F} \]

### Final Answer:
The capacitance of a spherical conductor with a radius of 1 meter is approximately:
\[ C \approx 1.1 \times 10^{-10} \, \text{F} \]