Question

An ideal spring has spring constant ks (to distinguish it from the electrostatic constant k) and equilibrium length l. Then, you glue two identical negative point charges to the ends of the spring and observe that the equilibrium length doubles. Determine the amount of charge on each end of the spring

Answer 1

q = square root (4KsL³/k)

The force of extension of the spring is equal to the force of repulsion between the two like charges. Two like charges(positive or negative) would always repel each other and two unlike charges would always attract each other. This electric force between the charges is what is responsible for the stretching of the spring. The electric force causes the spring to increase in length from L to 2L. Equating these forces, that is the electric force between the charges and the elastic force of the spring and rearranging the variables gives the expression to obtain q.

Step-by-step explanation:

See the attachment below for full solution.