Two spheres of radii r and R carry charges q and Q,...

Two spheres of radii $r$ and $R$ carry charges $q$ and $Q$, respectively. When they are connected by a wire, there will be no loss of energy of the system if
(A) $q r=Q R$
(B) $q R=Q r$
(C) $q r^{2}=Q R^{2}$
(D) $q R^{2}=O r^{2}$

Key Concepts

Electric Potential of a Conductor

This concept refers to the electric potential (voltage) on the surface of a conductor, which in the case of a sphere is determined by the amount of charge and its geometry. Specifically, for a sphere, the potential is directly proportional to the charge and inversely proportional to its radius. This relationship forms the basis for understanding how charges behave when conductors are connected.

Equipotential Principle

The equipotential principle states that in an ideal conductor in equilibrium, all parts of the conductor will have the same electric potential. When two conductors are connected by a wire, charge flows between them until their potentials are equal. This is crucial because if the conductors already have the same potential upon connection, there will be no flow of current, meaning no energy is dissipated as the system’s electrostatic configuration remains unchanged.

Energy Conservation in Electrostatic Systems

When charges redistribute between connected conductors, energy is often dissipated in the form of heat due to the flow of current. However, if the initial conditions are such that the connected conductors are already at the same potential (i.e., they satisfy the equipotential condition), there is no movement of charge and thus no energy loss. This concept is fundamental in ensuring that an ideal electrostatic system can adjust without the loss of stored energy.

Transcript

Please give Ace some feedback