A small charged plastic ball is vertically above another charged small ball in a frictionless 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 equilibrium distance between the balls in the test tube would become

Question

Quizplus · Accepted Answer

From Coulomb's Law, we know that the force between two point charges is inversely proportional to the square of the distance between them. If we double the charge on each ball, the force between them will be quadrupled (2²).

Since the balls are still in equilibrium, the force of gravity on each ball must be equal and opposite to the electrostatic force between them. Therefore, if the electrostatic force is quadrupled, the distance between the balls must be doubled (since the force of gravity remains the same).

Thus, the new equilibrium distance between the balls is 2d.

A Small Charged Plastic Ball Is Vertically Above Another Charged 2\sqrt { 2 }2​

A Small Charged Plastic Ball Is Vertically Above Another Charged $\sqrt { 2 }$