One Coulomb is defined as a charge which repels a similar charge at a distant of 1 m with the force of______________.

Options

A. `-9 xx 10^(-9)N`
B. `9 xx 10^(9)N`
C. `9 xx 102^(9) N`
D. `19 xx 10^(9)N`

Explanation

To solve the question, we need to determine the force exerted between two charges of 1 Coulomb each, separated by a distance of 1 meter. We will use Coulomb's Law, which states that the force \( F \) between two point charges is given by the formula:

\[ F = k \frac{q_1 q_2}{r^2} \]

where:
- \( F \) is the force between the charges,
- \( k \) is Coulomb's constant (\( k = \frac{1}{4\pi\epsilon_0} \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.

### Step 1: Identify the values
In this case:
- \( q_1 = 1 \, \text{C} \)
- \( q_2 = 1 \, \text{C} \)
- \( r = 1 \, \text{m} \)

### Step 2: Substitute the values into Coulomb's Law
Substituting the values into the formula, we get:

\[ F = k \frac{(1)(1)}{(1)^2} \]

### Step 3: Simplify the equation
This simplifies to:

\[ F = k \]

### Step 4: Substitute the value of \( k \)
The value of Coulomb's constant \( k \) is approximately \( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \). Thus:

\[ F = 9 \times 10^9 \, \text{N} \]

### Conclusion
Therefore, one Coulomb is defined as a charge which repels a similar charge at a distance of 1 meter with a force of \( 9 \times 10^9 \, \text{N} \).

### Final Answer
The answer is \( 9 \times 10^9 \, \text{N} \).

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