Physics
Physics
Problem
Two identical point charges are placed on a straight line symmetrically about a point in air. Initially each charge is at a distance from , and the electric potential at is 800 V. The charges are then moved farther apart so that each is now from ; the potential at becomes 500 V. (i) Calculate the initial distance (hence the initial separation between the charges). (ii) Determine the magnitude of each charge. Take .Intuitive explanation
The key insight is that electric potential at a point is a scalar sum of contributions from each charge, so you can write two equations relating the potential to the distance and charge magnitude. Since the charges are identical and symmetrically placed, their potential contributions simply add; by comparing the two potential values at different separations, you can solve for both the unknown distance and the charge . This is a system of two equations in two unknowns—algebra will do the heavy lifting once you set up the potential formula correctly.
Intuitive explanation
The key insight is that electric potential at a point is a scalar sum of contributions from each charge, so you can write two equations relating the potential to the distance and charge magnitude. Since the charges are identical and symmetrically placed, their potential contributions simply add; by comparing the two potential values at different separations, you can solve for both the unknown distance and the charge . This is a system of two equations in two unknowns—algebra will do the heavy lifting once you set up the potential formula correctly.