The relative permittivity of distilled water is 81. The velocity of light in it will be :
(Given `mu_(r )=1`)

Options

A. `4.33 xx 10^(7) m//s`
B. `2.33 xx 10^(7)m//s`
C. `3.33 xx 10^(7) m//s`
D. `5.33 xx 10^(7) m//s`

Answer

To find the velocity of light in distilled water given its relative permittivity, we can use the following formula:

\[ v = \frac{c}{\sqrt{\epsilon_r \mu_r}} \]

Where:
- \( v \) is the velocity of light in the medium,
- \( c \) is the speed of light in vacuum (approximately \( 3 \times 10^8 \) m/s),
- \( \epsilon_r \) is the relative permittivity of the medium,
- \( \mu_r \) is the relative permeability of the medium.

### Step-by-step Solution:

1. **Identify the values given in the problem:**
- Relative permittivity of distilled water, \( \epsilon_r = 81 \)
- Relative permeability, \( \mu_r = 1 \)

2. **Substitute the values into the formula:**
\[ v = \frac{c}{\sqrt{\epsilon_r \mu_r}} = \frac{3 \times 10^8}{\sqrt{81 \cdot 1}} \]

3. **Calculate the square root:**
\[ \sqrt{81} = 9 \]

4. **Substitute back into the equation:**
\[ v = \frac{3 \times 10^8}{9} \]

5. **Perform the division:**
\[ v = \frac{3}{9} \times 10^8 = \frac{1}{3} \times 10^8 \]

6. **Convert to a more manageable form:**
\[ v = 10 \times 10^7 \div 3 \approx 3.33 \times 10^7 \text{ m/s} \]

### Final Answer:
The velocity of light in distilled water is approximately \( 3.33 \times 10^7 \) m/s.

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