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

Question

Two identical metal balls are suspended by insulating threads. 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. Label the forces to indicate: the object exerting the force. the object on which the force is exerted, the type of force (gravitational, normal, etc.), and whether the force is a contact or a non-contact force. Suppose the charge on the second ball is reduced slightly, so that it is less than that on the first ball. Predict whether the angle that ball I makes with the vertical will be greater than, less than, or equal to the angle that ball 2 makes with the vertical. Explain. Sketch your answer at right. 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 are different, describe how they differ. Predict what will happen if the net charge on ball 2 is reduced to zero. Make a sketch to illustrate your answer.

Explanation / Answer

Here,

b)

Correct. The Coulomb force depends only on the product of the two charges and their spatial orientation, not the way the charge is distributed on each individual charge -- i.e., charges of 2 C and 8 C placed the same distance apart experience the same force as two charges of 4 C. Since the two setups are entirely symmetric, except for the charge on each sphere, each sphere experiences the same Coulomb force, as well as the same gravitational force, and consequently they make the same angle with the vertical (note, however, that since the total charge on the second ball is reduced, the new equilibrium angle will be less than that when both spheres had the same charge).

c)

If the charge is removed from one of the balls, Fe = k*q1*0/r^2 = 0 and both balls will hang at zero degrees with the vertical

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