`+2C` and `+6C` two charges are repelling each other with a force of `12N`. If each charges is given `-2C` of charge is given `-2C` of charge, then the value of the force will be

Options

A. `4N` (Attractive)
B. `4N` (Repulsive)
C. `8N` (Repulsive)
D. Zero

Explanation

To solve the problem, 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 (approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.

### Step 1: Identify the initial charges and the force
Initially, we have two charges:
- \( q_1 = +2C \)
- \( q_2 = +6C \)

The force between them is given as \( F = 12N \).

### Step 2: Determine the new charges after adding \(-2C\)
Each charge is given a charge of \(-2C\):
- New \( q_1 = +2C - 2C = 0C \)
- New \( q_2 = +6C - 2C = +4C \)

### Step 3: Calculate the new force
Now we have:
- \( q_1 = 0C \)
- \( q_2 = +4C \)

Using Coulomb's Law, the new force \( F' \) can be calculated as follows:

\[ F' = k \frac{|q_1 q_2|}{r^2} = k \frac{|0 \cdot 4|}{r^2} = k \frac{0}{r^2} = 0 \]

### Conclusion
The new force between the charges after giving each a charge of \(-2C\) is \( F' = 0N \).

### Final Answer
The value of the force will be \( 0N \).

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