Two conducting spheres of radii R 1 and R 2 having charges Q 1 and Q 2 respectively are placed very far…

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
  1. no change in the energy of the system
  2. an increase in the energy of the system
  3. always a decrease in the energy of the system
  4. a decrease in energy of the system unless q1R2 = q2R1

Solution

\(\begin{aligned} & \Delta U=\frac{1}{2}\left(\frac{C_1 C_2}{C_1+C_2}\right)\left(V_1-V_2\right)^2 \\ & \Delta U=0, \text { If } V_1=V_2 \\ & \text {or } \frac{k q_1}{R_1}=\frac{k q_2}{R_2} \\ & \text {or } q_1 R_2=q_2 R_1\end{aligned}\) ,

Asked in: JEE Mains - Electrostatics - Test 5

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