Two metallic charged spheres of radii R1 and R2 having...

Two metallic charged spheres of radii $R_{1}$ and $R_{2}$ having charges $Q_{1}$ and $Q_{2}$, respectively, are connected to each other. There is. a. no ch?nge in the energy of the system b. an increase in the energy of the system c. always a decrease in the energy of the system d. a decrease in energy of the system unless $Q_{1} R_{2}=Q_{2} R_{1}$

Two metallic charged spheres of radii $R_{1}$ and $R_{2}$ having charges $Q_{1}$ and $Q_{2}$, respectively, are connected to each other. There is.
a. no ch?nge in the energy of the system
b. an increase in the energy of the system
c. always a decrease in the energy of the system
d. a decrease in energy of the system unless $Q_{1} R_{2}=Q_{2} R_{1}$

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Key Concepts

Electrostatic Potential Equalization

When two conductors are connected, charges rearrange themselves until both conductors reach the same electric potential. This process is based on the principle that at equilibrium, there can be no current flow between conductors if they are at the same potential. In the case of charged spheres, this means that the initial charge distributions adjust to equalize their potentials.

Capacitance of Spherical Conductors

The capacitance of an isolated spherical conductor is determined by its radius, given by the formula C = 4???R. This concept is crucial because the potential (V) of each sphere is related to its charge (Q) and capacitance by V = Q/C. Thus, differences in radii cause different initial potentials for the same amount of charge, driving the redistribution when the spheres are connected.

Electrostatic Energy in Charge Redistribution

The energy stored in a charged conductor depends on both its charge and capacitance. When two charged spheres are connected and charges redistribute to equalize the potential, the overall electrostatic energy of the system decreases except in the special case where they are initially at the same potential. This loss in energy usually appears as heat due to the current flow during the redistribution process.

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