Two pith balls, each with a mass of 1.2 g, are attached to non-conducting threads and suspended from a common hook. Each thread has a length of 29.7 cm. The balls are then given an identical charge, which causes them to separate. In equilibrium, the threads are separated by an angle of 10.0°. Calculate the charge on each pith ball, in coulombs (C).

To solve this problem, we need to use Coulomb's Law and the formula for the tension in the strings.

Step 1: Identify the forces acting on the pith balls. There are two forces acting on each pith ball: the gravitational force (Fg) and the electrostatic force (Fe).

Step 2: Calculate the gravitational force. Fg = m*g where m is the mass of the pith ball (1.2 g = 0.0012 kg) and g is the acceleration due to gravity (9.8 m/s^2). Fg = 0.0012 kg * 9.8 m/s^2 = 0.01176 N

Step 3: Calculate the electrostatic force. The electrostatic force can be calculated using Coulomb's Law: Fe = kq1q2/r^2 where k is Coulomb's constant (8.9910^9 Nm^2/C^2), q1 and q2 are the charges on the pith balls (which are the same, so we can call this q), and r is the distance between the pith balls.

Step 4: Calculate the distance between the pith balls. The distance between the pith balls can be calculated using trigonometry. The pith balls and the point where the threads are attached form an isosceles triangle. The distance between the pith balls is the base of this triangle. We can calculate this distance using the formula: r = 2Lsin(θ/2) where L is the length of the thread (29.7 cm = 0.297 m) and θ is the angle between the threads (10.0°). r = 20.297 msin(10.0°/2) = 0.0518 m

Step 5: Set the gravitational force equal to the electrostatic force and solve for q. Fg = Fe 0.01176 N = (8.9910^9 Nm^2/C^2)q^2/(0.0518 m)^2 Solving this equation for q gives: q = sqrt((0.01176 N * (0.0518 m)^2) / (8.9910^9 Nm^2/C^2)) = 1.6110^-8 C

So, the charge on each pith ball is 1.61*10^-8 C.