Two point charges +5 $\mu C$ and -5 $\mu C$ are placed at O (0 mm, 0mm) and P(3 mm, 4 mm) respectively force on $+5 \mu C$ is

$1.8(3\hat{i}+4\hat{j})\times 10^{3} N$

The correct answer is option (3) : $1.8(3\hat{i}+4\hat{j})\times 10^{3} N$

Step 1: Identify charges and positions

• +5 μC at O (0, 0)
• –5 μC at P (3 mm, 4 mm)

Step 2: Direction of force
Since charges are opposite, force is attractive, so it acts from O towards P.

Direction vector = 3î + 4ĵ

Step 3: Distance between charges
r = √(3² + 4²) = 5 mm = 5 × 10⁻³ m

Step 4: Unit vector
r̂ = (3î + 4ĵ) / 5

Step 5: Apply Coulomb’s law
F = k |q₁q₂| / r²

= (9 × 10⁹ × 5 × 10⁻⁶ × 5 × 10⁻⁶) / (5 × 10⁻³)²

= (9 × 25 × 10⁻³) / 25 × 10⁻⁶

= 9 × 10³ 

= 9 × 10³ N

Step 6: Write vector form
F⃗ = magnitude × unit vector

= 9× 10³ × (3î + 4ĵ)/5

= 1.8(3î + 4ĵ) × 10³ N