Figure shows a solid metal sphere of radius a surrounded by a concentric thin metal shell of radius 2a. Initially both are having charges Q each. When the two are connected by a conducting wire as shown in figure, then amount of heat produced in this process will be $\frac{kQ^2}{\lambda a}$ . Find the value of λ.
Your answer

Question

Figure shows a solid metal sphere of radius a surrounded by a concentric thin metal shell of radius 2a. Initially both are having charges Q each. When the two are connected by a conducting wire as shown in figure, then amount of heat produced in this process will be $\frac{kQ^2}{\lambda a}$ . Find the value of λ.

Your answer

G1 Physics · Accepted Answer

Step 1: In electrostatic equilibrium, E = 0 inside a conductor and the conductor is an equipotential. Surface charges adjust so the boundary condition field just outside·𝐧 = σ/ε₀ is satisfied. Step 2: For connected conductors set their potentials equal; for sheets use electrostatic pressure p = ε₀E²/2 when appropriate. Step 3: Apply charge conservation and the given geometry. Final: 4.