The radius of spherical capacitor when capacitance is `1 muF` is:

Options

A. `1*11 m`
B. 9 km
C. 10 m
D. `1*11 cm`

Explanation

To find the radius of a spherical capacitor with a capacitance of \(1 \, \mu F\), we can use the formula for the capacitance of a spherical capacitor. The capacitance \(C\) of a spherical capacitor is given by the formula:

\[ C = \frac{4 \pi \epsilon_0 r}{1} \]

where:
- \(C\) is the capacitance,
- \(r\) is the radius of the spherical capacitor,
- \(\epsilon_0\) is the permittivity of free space, approximately \(8.85 \times 10^{-12} \, F/m\).

### Step 1: Rearranging the formula for \(r\)

From the capacitance formula, we can rearrange it to solve for the radius \(r\):

\[ r = \frac{C}{4 \pi \epsilon_0} \]

### Step 2: Substituting the values

Now we can substitute the given value of capacitance \(C = 1 \, \mu F = 1 \times 10^{-6} \, F\) and the value of \(\epsilon_0\):

\[ r = \frac{1 \times 10^{-6}}{4 \pi (8.85 \times 10^{-12})} \]

### Step 3: Calculating the denominator

Calculating the denominator:

\[ 4 \pi \epsilon_0 \approx 4 \times 3.14 \times 8.85 \times 10^{-12} \approx 1.112 \times 10^{-10} \, F \]

### Step 4: Completing the calculation

Now substituting this back into our equation for \(r\):

\[ r = \frac{1 \times 10^{-6}}{1.112 \times 10^{-10}} \approx 8.99 \times 10^{3} \, m \]

### Step 5: Converting to kilometers

To convert meters to kilometers, we divide by \(1000\):

\[ r \approx 8.99 \, km \]

### Final Result

Thus, the radius of the spherical capacitor is approximately \(9 \, km\).