Two point charges of equal magnitude but opposite sign
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
Two point charges of equal magnitude but opposite sign, +q and −q, are held a fixed distance r apart in air (assume vacuum permittivity). The zero of electric potential energy is taken at infinite separation. The charges are then slowly and carefully lowered, without changing their positions relative to each other, into fresh water, whose dielectric constant is εr=80. Throughout the entire procedure the separation r remains constant.
Respond to all parts thoroughly, showing algebraic reasoning and clearly labeled steps.
(a) Obtain an algebraic expression for the electric potential energy of the two-charge system while it is still in air.
(b) Write a corresponding expression for the potential energy after the system is fully submerged in the water.
(c) Calculate the ratio Uwater/Uair and state whether the magnitude of the energy increases or decreases upon submersion.
(d) If the submersion is carried out quasi-statically (very slowly) by an external agent, determine the work done by the agent during the process in terms of q, r, and fundamental constants, and indicate the sign of that work.
(e) Based on your answer to part (d), discuss whether the external agent must supply energy to the system or remove energy from it, and relate this to the behavior of the electric forces during the submersion.