PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
Two identical positive point charges, each of magnitude q, are fixed on the x-axis at x=0 and x=d, where d is a known constant. A third small positive test charge q0 is free to move along the x-axis between the fixed charges. All other forces are negligible.
(a) Derive an algebraic expression for the electric potential energy U(x) of the three-charge system as a function of the position x (0<x<d) of the test charge.
(b) On the axes you will provide, sketch U(x) for 0<x<d. Clearly label the shape’s key features, including any extrema and symmetry.
(c) Determine the position xeq (in terms of d) at which the net electric force on the test charge is zero. Show your reasoning.
(d) Using your graph and the expression from part (a), classify the equilibrium at xeq as stable or unstable and justify your classification with explicit reference to energy considerations.