A long, hollow conducting cylindrical shell is mounted horizontally on an insulating…
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
A long, hollow conducting cylindrical shell is mounted horizontally on an insulating support. The shell is initially neutral and is connected to ground by a removable wire. A thin positively charged rod is inserted along the axis of the cylinder without touching the inner surface and held fixed. The following operations are then performed in two different sequences:
• Sequence X: The grounding wire is first disconnected while the charged rod remains in place. Afterward, the charged rod is removed completely from the cylinder.
• Sequence Y: The charged rod is first withdrawn from the cylinder while the grounding wire remains attached. After the rod is far away, the grounding wire is disconnected.
Assume the system is isolated from external charges, edge effects are negligible, and the process is slow enough to ignore induced currents.
(a) For Sequence X, identify the sign of the induced charge on the inner and outer surfaces of the cylindrical shell after the grounding wire has been disconnected but before the charged rod is removed. Explain your reasoning.
(b) For Sequence X, determine the net charge on the shell after the charged rod has been removed. Provide a clear explanation based on charge conservation.
(c) Repeat parts (a) and (b) for Sequence Y.
(d) Compare the final net charges on the shell for the two sequences. Explain why the order of operations leads to different or identical outcomes, citing relevant physical principles.