Two insulated charged metallic spheres P and Q have their centres separated by a distance of 60 cm. The radii of P and Q are negligible compared to the distance of separation. The mutual force of electrostatic repulsion if the charge on each is `3.2xx10^(-7)C` is

Options

A. `5.2xx10^(-4)N`
B. `2.56xx10^(-3)N`
C. `1.5xx10^(-3)N`
D. `3.5xx10^(-4)N`

Explanation

To find the mutual force of electrostatic repulsion between two charged metallic spheres P and Q, we can use Coulomb's law, which states that the force \( F \) between two point charges is given by:

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

where:
- \( F \) is the electrostatic force,
- \( k \) is Coulomb's constant (\( 9 \times 10^9 \, \text{N m}^2/\text{C}^2 \)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the centers of the two charges.

### Given:
- Distance \( r = 60 \, \text{cm} = 0.6 \, \text{m} \)
- Charge on each sphere \( q_1 = q_2 = 3.2 \times 10^{-7} \, \text{C} \)

### Step 1: Substitute the values into Coulomb's law
We can substitute the values into the formula:

\[ F = k \frac{q_1 q_2}{r^2} \]
\[ F = 9 \times 10^9 \frac{(3.2 \times 10^{-7}) (3.2 \times 10^{-7})}{(0.6)^2} \]

### Step 2: Calculate \( (3.2 \times 10^{-7})^2 \)
Calculating \( (3.2 \times 10^{-7})^2 \):

\[ (3.2 \times 10^{-7})^2 = 10.24 \times 10^{-14} = 1.024 \times 10^{-13} \]

### Step 3: Calculate \( (0.6)^2 \)
Calculating \( (0.6)^2 \):

\[ (0.6)^2 = 0.36 \]

### Step 4: Substitute back into the equation
Now substituting back into the equation:

\[ F = 9 \times 10^9 \frac{1.024 \times 10^{-13}}{0.36} \]

### Step 5: Calculate the fraction
Calculating \( \frac{1.024 \times 10^{-13}}{0.36} \):

\[ \frac{1.024 \times 10^{-13}}{0.36} \approx 2.8444 \times 10^{-13} \]

### Step 6: Multiply by \( 9 \times 10^9 \)
Now multiply by \( 9 \times 10^9 \):

\[ F \approx 9 \times 10^9 \times 2.8444 \times 10^{-13} \approx 2.56 \times 10^{-3} \, \text{N} \]

### Final Result
Thus, the mutual force of electrostatic repulsion between the two charged spheres is:

\[ F \approx 2.56 \times 10^{-3} \, \text{N} \]