Final answer:
The question requires using principles of electrostatics and Newton's laws to solve for the charge on Styrofoam balls in equilibrium hung in the form of an equilateral triangle.
Step-by-step explanation:
The question involves applying concepts from electrostatics and Newton's laws of motion to determine the charge on the styrofoam balls. To begin with, we recognize that the balls are in both mechanical and electrostatic equilibrium. Each ball experiences two electrostatic forces due to the repulsion from the other two charged balls, and these forces must sum to provide a net force that is balanced by the tension in the thread.
By using Coulomb's law for the electric force between two charges (F = k * |q1 * q2| / r^2) and the fact that the net force has to counteract the gravitational force (mg), we can set up an equation to solve for the charge q on each ball. Additionally, the geometry of the system suggests that the components of the electrostatic forces in the horizontal plane will sum to zero, maintaining the balls in an equilateral triangle, and the vertical component will balance the weight.
Once the Coulomb forces are calculated and sum together for the equilibrium condition, they can be equated with the gravitational force to solve for the magnitude of the charge q. The final formula may involve constants such as the Coulomb constant (k), the distance between the balls (r), and the mass (m) of the balls. Note that the angle formed by the strings and the vertical direction will also come into play in the force balance.