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 when the capacitance is given as 1 microfarad (1 µF), we can use the formula for the capacitance of a spherical capacitor. The capacitance \( C \) of a spherical capacitor is given by:

\[ C = 4\pi \epsilon_0 \frac{R_1 R_2}{R_2 - R_1} \]

For a spherical capacitor with an inner radius \( R_1 \) and an outer radius \( R_2 \), if we assume \( R_1 \) is negligible compared to \( R_2 \) (which is a common assumption for large capacitors), we can simplify the formula to:

\[ C \approx 4\pi \epsilon_0 R \]

where \( R \) is the radius of the outer sphere, and \( \epsilon_0 \) (the permittivity of free space) is approximately \( 8.85 \times 10^{-12} \, \text{F/m} \).

Given that the capacitance \( C = 1 \, \mu\text{F} = 1 \times 10^{-6} \, \text{F} \), we can rearrange the formula to find \( R \):

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

Substituting the values:

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

Calculating the denominator:

\[ 4\pi \times 8.85 \times 10^{-12} \approx 1.112 \times 10^{-10} \]

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

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

Thus, the radius \( R \) is approximately \( 8.99 \, \text{km} \).

### Final Answer:
The radius of the spherical capacitor when the capacitance is 1 µF is approximately **9 km**.

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