Two conducting spheres of radii R1 and R2 having charges Q1 and Q2 respectively are placed very far apart from each other. Now they are connected to each other by a connecting wire, then there is

Question

Two conducting spheres of radii R1 and R2 having charges Q1 and Q2 respectively are placed very far apart from each other. Now they are connected to each other by a connecting wire, then there is (A) no change 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 q1R2 = q2R1

Tardigrade Admin · Accepted Answer

Δ U = (1/2) ((C1 C2/C1 + C2)) (V1 - V2)2 Δ U = 0 , If V1 = V2 or (k q1/R1) = (k q2/R2) or q1R2=q2R1

Q. Two conducting spheres of radii $R_{1}$ and $R_{2}$ having charges $Q_{1}$ and $Q_{2}$ respectively are placed very far apart from each other. Now they are connected to each other by a connecting wire, then there is

no change in the energy of the system

an increase in the energy of the system

always a decrease in the energy of the system

a decrease in energy of the system unless $q_{1} R_{2} = q_{2} R_{1}$

$Δ U = \frac{1}{2} (\frac{C _{1} C _{2}}{C _{1} + C _{2}}) (V_{1} - V_{2})^{2}$
$Δ U = 0$ , If $V_{1} = V_{2}$
or $\frac{k q _{1}}{R _{1}} = \frac{k q _{2}}{R _{2}}$
or $q_{1} R_{2} = q_{2} R_{1}$

Q. Two conducting spheres of radii R1​ and R2​ having charges Q1​ and Q2​ respectively are placed very far apart from each other. Now they are connected to each other by a connecting wire, then there is