PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
Two identical point charges, each of magnitude Q and sign −Q, are fixed on the y-axis at y=+d and y=−d. A small positive test charge +q is initially at a very large distance along the positive x-axis. The charge is moved slowly (so that kinetic energy remains negligible) to the origin (0,0).
(a) Derive an algebraic expression for the electric potential at the origin due to the two fixed charges in terms of Q, d, and physical constants.
(b) Using your result from part (a), obtain a symbolic expression for the work that must be done by an external agent to bring the test charge from infinity to the origin.
(c) Find the coordinate x0 on the positive x-axis where the magnitude of the potential due to the two fixed charges is exactly one-half of the magnitude at the origin. Express x0 in terms of d.
(d) Discuss qualitatively how both the potential at the origin and the external work required in part (b) would change if the fixed charges were instead +Q (identical in magnitude but opposite in sign).