The force between two charges 0.06m apart is 5N. If each charge is moved towards the other by 0.01 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 will use Coulomb's law, which states that the force \( F \) between two point charges is inversely proportional to the square of the distance \( R \) between them.

### Step 1: Identify the initial conditions
We know the initial distance \( R_1 \) between the two charges is 0.06 m and the initial force \( F_1 \) is 5 N.

### Step 2: Determine the new distance after moving the charges
Both charges are moved towards each other by 0.01 m. Therefore, the new distance \( R_2 \) is:
\[ R_2 = R_1 - 0.01 - 0.01 = 0.06 - 0.02 = 0.04 \text{ m} \]

### Step 3: Apply Coulomb's law
According to Coulomb's law, the relationship between the forces and distances can be expressed as:
\[ \frac{F_1}{F_2} = \frac{R_2^2}{R_1^2} \]

### Step 4: Rearrange the equation to find \( F_2 \)
We can rearrange the equation to solve for \( F_2 \):
\[ F_2 = F_1 \cdot \frac{R_1^2}{R_2^2} \]

### Step 5: Substitute the known values
Substituting \( F_1 = 5 \) N, \( R_1 = 0.06 \) m, and \( R_2 = 0.04 \) m into the equation:
\[ F_2 = 5 \cdot \frac{(0.06)^2}{(0.04)^2} \]

### Step 6: Calculate \( R_1^2 \) and \( R_2^2 \)
Calculating the squares:
\[ (0.06)^2 = 0.0036 \quad \text{and} \quad (0.04)^2 = 0.0016 \]

### Step 7: Substitute back into the equation
Now substituting these values back into the equation for \( F_2 \):
\[ F_2 = 5 \cdot \frac{0.0036}{0.0016} \]

### Step 8: Simplify the fraction
Calculating the fraction:
\[ \frac{0.0036}{0.0016} = 2.25 \]

### Step 9: Calculate the final force
Now substituting this back:
\[ F_2 = 5 \cdot 2.25 = 11.25 \text{ N} \]

### Conclusion
Thus, the new force \( F_2 \) between the charges after they are moved closer together is **11.25 N**.