Students perform an experiment to determine the value of vacuum permittivity ε₀. Sphere 1 is nonconducting with charge +q and is attached to an insulating rod. Sphere 2 is nonconducting with charge +Q and has mass M. Sphere 2 is hung from a string of negligible mass and length L. Sphere 1 is brought near, without touching, Sphere 2 as shown. Equilibrium is established when the centers of the two spheres have the same vertical position, are a horizontal distance d apart, and the string is at an angle θ from the vertical.
b. Now derive the relationship between the distance d and the angle theta to show that d = √((Qq)/(4πε₀Mgtan(θ))). BY THE WAY, ε is the vacuum permittivity ε₀.
c. These values are collected in one trial: Q=q=6*10^(-8) C, θ = 12°, and d = 0.057 m. Calculate the expected force of tension exerted on sphere 2 by the string.