1. Understand the Concepts

* Electrostatic Force: The force of attraction or repulsion between charged objects at rest.

* Coulomb's Law: The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

* F = (k * q1 * q2) / r²

* F = electrostatic force

* k = Coulomb's constant (8.98755 × 10⁹ N⋅m²/C²)

* q1, q2 = magnitudes of the charges

* r = distance between the charges

2. Convert Units

* Microcoulombs (µC) to Coulombs (C):

* 200 µC = 200 × 10⁻⁶ C

* 500 µC = 500 × 10⁻⁶ C

* Grams-force (gf) to Newtons (N):

* 5 gf = 5 × 9.8 × 10⁻³ N (Since 1 gf ≈ 9.8 × 10⁻³ N)

3. Set up the Equation

We know:

* F = 5 × 9.8 × 10⁻³ N

* q1 = 200 × 10⁻⁶ C

* q2 = 500 × 10⁻⁶ C

* k = 8.98755 × 10⁹ N⋅m²/C²

We need to find 'r'.

4. Solve for 'r'

* Rearrange Coulomb's Law to solve for 'r':

* r² = (k * q1 * q2) / F

* r = √((k * q1 * q2) / F)

* Plug in the values:

* r = √((8.98755 × 10⁹ N⋅m²/C² * 200 × 10⁻⁶ C * 500 × 10⁻⁶ C) / (5 × 9.8 × 10⁻³ N))

* r ≈ 1.34 meters

Therefore, the distance between the two charges is approximately 1.34 meters.