Suppose you hung two pith balls from long insulating strings of length L = 20 cm. You then touched the pith balls with a charged Teflon rod, causing them both to become equally charged. The pith balls are seen to repel each other and hang a distance d=2.0 cm apart. The mass of each pith ball is m = 0.30 g. Ignore the mass of the strings.

The goal is to determine the magnitude of the electric force on each ball, and from this, to determine the electric charge on each ball and the electric field that one ball creates.

1. Free-body diagram On a piece of paper, reproduce the diagram shown, and then draw a free-body diagram for each pith ball. Each diagram should have three force vectors. Use your diagrams as a guide to answer the following questions.

In the small angle approximation where sin θ≈θ, what equation in the variables L and d gives θ?

Because the pith ball is stationary, the sum of the force vectors must equal zero. Thus, there is also a mathematical relationship between the magnitude of the weight of the pith ball mg and the magnitude of the electric force F from the other pith ball. In the small angle approximation, where (in this case) tan θ≈θ, what equation in the variables mg and F also gives θ?

2. Electrostatic force Set the two equations you have just found to be equal to each other and solve for the magnitude of the electrical force in terms of the other variables:

Use your formula and the data given to calculate F (include units and assume g= 9.81 m/s²)

3. Electric field

Assume that the two balls are point charges at the end of the strings and calculate the magnitude of the charge q on one of the balls by using Coulomb's law (include units and let k= 8.99 x10⁹ N m²/C²).

If you let the pith ball on the right be considered a "lest charge", what is the magnitude of the electric field E at the location of the test charge that is created by the charge on the pith ball located on the left (include units)?