if the capacity of a spherrical conductor is 1 `muF`, the diameter of the conductor will be

Options

A. `1.2xx10^(4)m`
B. `1.8xx10^(4)m`
C. `2.4xx10^(4)m`
D. `3xx10^(4)m`

Explanation

To find the diameter of a spherical conductor given its capacitance, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The capacitance \( C \) of the spherical conductor is given as \( 1 \, \mu F \).
- Convert microfarads to farads:
\[ C = 1 \, \mu F = 1 \times 10^{-6} \, F \]

2. **Recall the Formula for Capacitance of a Spherical Conductor**:
- The formula for the capacitance \( C \) of a spherical conductor is given by:
\[ C = 4 \pi \epsilon_0 r \]
where \( r \) is the radius of the sphere and \( \epsilon_0 \) is the permittivity of free space.

3. **Substitute the Known Values**:
- We need to find the radius \( r \). Rearranging the formula gives:
\[ r = \frac{C}{4 \pi \epsilon_0} \]
- The value of \( \epsilon_0 \) is approximately \( 8.85 \times 10^{-12} \, F/m \).

4. **Calculate \( r \)**:
- Substitute the values into the equation:
\[ r = \frac{1 \times 10^{-6}}{4 \pi (8.85 \times 10^{-12})} \]
- Calculate \( 4 \pi \epsilon_0 \):
\[ 4 \pi \epsilon_0 \approx 4 \times 3.14 \times 8.85 \times 10^{-12} \approx 1.11 \times 10^{-10} \, F/m \]
- Now substituting this back:
\[ r = \frac{1 \times 10^{-6}}{1.11 \times 10^{-10}} \approx 9.01 \times 10^{3} \, m \]

5. **Calculate the Diameter \( d \)**:
- The diameter \( d \) is given by:
\[ d = 2r \]
- Substitute the value of \( r \):
\[ d = 2 \times 9.01 \times 10^{3} \approx 1.80 \times 10^{4} \, m \]

### Final Answer:
The diameter of the spherical conductor is approximately \( 1.80 \times 10^{4} \, m \).