Calculate force between two charges of 1C each separated by 1m in vacuum.

Options

A. `9 xx 10^(9) N`
B. `0.9 xx 10^(-9)N`
C. `9 xx 10^(-9)N`
D. `9 xx 10^(9)` dyne

Answer

To calculate the force between two charges of 1C each separated by 1m in vacuum, we can use Coulomb's Law, which states that the electric force (F) between two point charges is given by the formula:

\[ F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2} \]

Where:
- \( F \) is the electric force between the charges,
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges,
- \( \epsilon_0 \) is the permittivity of free space, approximately equal to \( 8.85 \times 10^{-12} \, \text{C}^2/\text{N m}^2 \).

### Step-by-Step Solution:

1. **Identify the values:**
- Given \( q_1 = 1 \, \text{C} \)
- Given \( q_2 = 1 \, \text{C} \)
- Given \( r = 1 \, \text{m} \)

2. **Substitute the values into the formula:**
\[ F = \frac{1}{4 \pi \epsilon_0} \frac{(1)(1)}{(1)^2} \]

3. **Simplify the equation:**
\[ F = \frac{1}{4 \pi \epsilon_0} \]

4. **Use the value of \( \frac{1}{4 \pi \epsilon_0} \):**
- The value of \( \frac{1}{4 \pi \epsilon_0} \) is approximately \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \).

5. **Calculate the force:**
\[ F = 9 \times 10^9 \, \text{N} \]

### Final Answer:
The electric force between the two charges is \( 9 \times 10^9 \, \text{N} \).

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