One very small uniformly charged plastic ball is located directly above another such charge in a test tube as shown in the figure. The balls are in equilibrium a distance d apart. If the charge on each ball is doubled, the distance between the balls in the test tube would become

Question

Quizplus · Accepted Answer

According to Coulomb's law, the electric force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. If the charges are doubled, the electric force between them will also be doubled. For the two charged balls to remain in equilibrium, the force of repulsion between them must be balanced by the gravitational force pulling them together. Since the gravitational force remains constant, the electric force must be balanced by an increase in the distance between the balls. If the distance is multiplied by a factor x, the electric force will be divided by x^2, so one would need to find x such that (1/x^2) = 2. Solving for x, we get x = √2. Therefore, the new distance between the balls is d√2 or approximately 1.4d. So, the answer is option B, 2d.

One Very Small Uniformly Charged Plastic Ball Is Located Directly