The force between two charges `0.06m` apart is `5N`. If each charge is moved towards the other by `0.04 m`, then the force between them will become

Options

A. 7.20 N
B. 11.25 N
C. 22.50 N
D. 45.00 N

Answer

To solve the problem step by step, we need to use Coulomb's law, which states that the force \( F \) between two point charges is given by the formula:

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

where:
- \( F \) is the force between the charges,
- \( k \) is Coulomb's constant,
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.

### Step 1: Identify the initial conditions
We are given:
- The initial distance \( r = 0.06 \, m \)
- The initial force \( F = 5 \, N \)

### Step 2: Determine the new distance
Each charge is moved towards the other by \( 0.04 \, m \). Therefore, the new distance \( r' \) is calculated as follows:

\[ r' = r - 0.04 - 0.04 = 0.06 - 0.08 = 0.02 \, m \]

### Step 3: Write the expression for the new force
Using Coulomb's law again for the new distance, we have:

\[ F' = \frac{k \cdot q_1 \cdot q_2}{(r')^2} \]

### Step 4: Relate the initial and new forces
Since \( k \), \( q_1 \), and \( q_2 \) remain constant, we can write the ratio of the forces:

\[ \frac{F}{F'} = \frac{r'^2}{r^2} \]

### Step 5: Substitute the known values
Substituting the known values into the ratio:

\[ \frac{5 \, N}{F'} = \frac{(0.02)^2}{(0.06)^2} \]

Calculating \( (0.02)^2 \) and \( (0.06)^2 \):

\[ (0.02)^2 = 0.0004 \quad \text{and} \quad (0.06)^2 = 0.0036 \]

Now substituting these values into the equation:

\[ \frac{5}{F'} = \frac{0.0004}{0.0036} \]

### Step 6: Solve for \( F' \)
Cross-multiplying gives:

\[ 5 \cdot 0.0036 = F' \cdot 0.0004 \]

Calculating \( 5 \cdot 0.0036 \):

\[ 0.018 = F' \cdot 0.0004 \]

Now, divide both sides by \( 0.0004 \):

\[ F' = \frac{0.018}{0.0004} = 45 \, N \]

### Step 7: Final calculation
Thus, the new force \( F' \) is:

\[ F' = 45 \, N \]

### Conclusion
The force between the charges after they are moved closer will become \( 45 \, N \).