Calculate the magnitude of force between two like charges each of magnitude 4C seperated by distance 3 m.

Answer

To calculate the magnitude of the force between two like charges, we can 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 (\( k = 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.

### Step 1: Identify the values
Given:
- \( q_1 = q_2 = 4 \, \text{C} \) (both charges are equal),
- \( r = 3 \, \text{m} \).

### Step 2: Substitute the values into the formula
Substituting the values into the formula, we have:

\[ F = k \frac{q_1 q_2}{r^2} = 9 \times 10^9 \frac{(4)(4)}{(3)^2} \]

### Step 3: Calculate \( r^2 \)
Calculate \( r^2 \):

\[ r^2 = 3^2 = 9 \]

### Step 4: Substitute \( r^2 \) back into the formula
Now substitute \( r^2 \) back into the equation:

\[ F = 9 \times 10^9 \frac{16}{9} \]

### Step 5: Simplify the expression
Now simplify the expression:

\[ F = 9 \times 10^9 \times \frac{16}{9} \]

The \( 9 \) in the numerator and denominator cancels out:

\[ F = 16 \times 10^9 \, \text{N} \]

### Step 6: Final Result
Thus, the magnitude of the force between the two like charges is:

\[ F = 16 \times 10^9 \, \text{N} \]