Two insulated charged spheres of radii R1 and R2 having charges Q1 and Q2 , respectively, are connected to each other; then there is

Question

Two insulated charged spheres of radii R1 and R2 having charges Q1 and Q2 , respectively, are connected to each other; 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

Decrease in energy of the system after connection is given by 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 insulated charged spheres of radii $R_{1}$ and $R_{2}$ having charges $Q_{1}$ and $Q_{2}$ , respectively, are connected to each other; 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 $q_{1} R_{2} = q_{2} R_{1}$

Decrease in energy of the system after connection is given by
$Δ U = \frac{1}{2} (\frac{C _{1} C _{2}}{C _{1} + C _{2}}) (V_{1} - V_{2})^{2}$
$Δ U = 0,$ 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 insulated charged spheres of radii R1​ and R2​ having charges Q1​ and Q2​ , respectively, are connected to each other; then there is