A single, irregularly shaped conducting object is placed in a region where an…
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
A single, irregularly shaped conducting object is placed in a region where an external uniform electric field points vertically downward. After a long time, the charges on the conductor have reached electrostatic equilibrium. Three locations on the surface are identified:
• Point P is a sharp upward-pointing tip.
• Point Q lies on a relatively flat vertical face.
• Point R lies in a small concave indentation on the underside.
(a) Rank the magnitude of the surface charge density σ at points P, Q, and R from greatest to smallest. Clearly indicate any equalities.
(b) Provide a detailed explanation for your ranking, making explicit reference to electric field lines, field strength just outside the surface, and the requirement for electrostatic equilibrium on a conductor.
(c) A tiny neutral conducting probe is brought very close (but not touching) to the conductor at point Q. Describe the direction and relative magnitude of the net electrostatic force experienced by the probe, and explain how it compares with the force the probe would experience near point P.
(d) Discuss how, if at all, the total net charge on the conductor changes as a consequence of being placed in the external electric field. Justify your answer in terms of charge conservation.