Two identical small spheres each of mass are suspended from a common point by two…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Two identical small spheres each of mass m=0.80g are suspended from a common point by two non-conducting threads of length L=0.50m. Each sphere is given the same positive charge q so that the threads make equal angles θ with the vertical at static equilibrium.
Initially the system is in a vacuum, and the measured separation between the spheres is x0=0.12m. The entire apparatus is then completely immersed in a non-conducting oil of relative permittivity εr=4.2, with all other conditions unchanged.
Assume the charges remain fixed on the spheres and the densities of the spheres and oil are such that buoyant forces are negligible.
Address the following prompts.
(a) Starting from force equilibrium considerations, derive an expression for tanθ in terms of q, m, L, εr, and fundamental constants for a homogeneous dielectric medium.
(b) Using the measured separation x0 in vacuum, determine the initial value of θ and calculate the magnitude of the charge q on each sphere.
(c) Predict the new equilibrium separation x of the spheres once they are submerged in the oil. Show all steps in your calculation.
(d) Explain qualitatively how the polarization of the oil molecules leads to the change in x, and discuss any practical limitations of using this setup to measure large permittivities.