Two identical metal balls are suspended by insulating strings. Both balls have t

Question

Two identical metal balls are suspended by insulating strings. Both balls have the same net charge. In this problem, do not assume the balls are point charges. Draw a separate free-body diagram for each ball. Predict what will happen if the charge on the second ball is reduced slightly, so it is less than that on the first ball. Draw a sketch to illustrate your answer. How does the free-body diagram for each ball in this case compare to the corresponding free-body diagram that you drew in part( a) If the magnitudes or directions of any of the forces change, explain how they change.

Explanation / Answer

a) The force between the balls will be kq^2/r^2 where r is the distance between them and q is the charge on each. The strings will make equal angles with the vertical. Two forces are on each ball, weight and the force of repulsion due to their charges. Both strings will hang at the same angle theta with the vertical. Tan(theta) = Fe/mg where Fe = kq^2/r^2 and mg is the weight of the ball.
b & c) Reducing the charge on one ball will cause Fe to decrease, reducing the angle each string makes with the vertical. Both strings will still make the same angle with the vertical but that angle will be smaller because Fe = kq1q2/r^2 will be weaker. The angles are equal because the weight of each ball is unchanged.

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