Understanding the Concepts

* Electric Field: An electric field exerts a force on charged particles. The direction of the force depends on the sign of the charge and the direction of the electric field.

* Free Fall: An object in free fall experiences only the force of gravity. If the particle remains suspended, there must be an upward force equal to the force of gravity.

Calculations

1. Force of Gravity:

* Mass of the particle (m) = 2 mg = 2 x 10^-6 kg

* Acceleration due to gravity (g) = 9.8 m/s²

* Force of gravity (Fg) = m * g = (2 x 10^-6 kg) * (9.8 m/s²) = 1.96 x 10^-5 N

2. Electric Force:

* The electric force (Fe) must be equal in magnitude but opposite in direction to the force of gravity to keep the particle suspended.

* Fe = Fg = 1.96 x 10^-5 N

3. Charge of the Particle:

* Electric force (Fe) = q * E, where q is the charge and E is the electric field strength.

* q = Fe / E = (1.96 x 10^-5 N) / (4 N/C) = 4.9 x 10^-6 C

Nature of the Charge

Since the electric field is directed upwards, and the particle is suspended, the electric force must also be directed upwards. This means the charge on the particle must be positive.

Conclusion

The charge on the particle is 4.9 x 10^-6 Coulombs, and it is positive.