Final answer:
The equilibrium height of the mobile charge is approximately 0.96 meters.
Step-by-step explanation:
The equilibrium height of the mobile charge can be determined by setting the Coulomb force equal to the weight of the charge. The Coulomb force between two charges is given by the equation:
F = k * (q1 * q2) / r^2
In this case, the Coulomb force between the two charges is equal to the weight of the mobile charge, which is given by:
F = m * g
Setting the two forces equal to each other and solving for the height, we get:
h = sqrt(k * (q1 * q2) / (m * g))
Plugging in the given values of q1 = 10 nC, q2 = 50 nC, m = 50 g, and g = 9.8 m/s^2, we can calculate the equilibrium height.
h = sqrt((9 * 10^9 Nm^2/C^2) * (10 * 10^-9 C * 50 * 10^-9 C) / (0.05 kg * 9.8 m/s^2))
h = sqrt(45 * 10^-6 / (0.05 * 9.8))
h = sqrt(0.9184)
h ≈ 0.96 meters