Two small spheres, each with a mass of 20 g , are hung from a common point by two insulating strings, each 40 cm long. The spheres carry identical charges, and the equilibrium separation between the balls is observed to be 4 cm . Determine the charge on each sphere.

Step-by-step solution

Let the charge on each sphere be q . The forces acting on each sphere in equilibrium are the tension T in the string, the weight mg acting downwards, and the electrostatic force of repulsion F_e acting horizontally. Resolving the tension into horizontal and vertical components: T = F_e T = mg Dividing the two equations, we get: = F_e mg From the geometry of the arrangement, the distance of each sphere from the vertical axis is x 2 = 4 cm 2 = 2 cm = 0.02 m . Since the angle is very small, = 0.02 0.40 = 0.05 . The el