Question

If we place a charged sphere in a metal box then the metal block is earthed the potential of sphere will ?? Inc or dec

Answer 1

Dec

Answer 2

When a charged sphere is placed inside a metal box, and the box is earthed, the potential of the box becomes zero. Due to electrostatic induction, an opposite charge is induced on the inner surface of the box. This induced charge, being closer to the sphere than infinity, effectively reduces the net potential at the sphere's surface. Specifically, the potential of the sphere changes from $V_{initial} = kQ/r_s$ to $V_{final} = kQ(1/r_s - 1/R_i)$. Since $R_i > r_s$, the term $kQ/R_i$ is subtracted from the initial potential. If $Q$ is positive, $V_{final} < V_{initial}$, meaning the potential decreases. If $Q$ is negative, $V_{final} > V_{initial}$, meaning the potential increases (becomes less negative). However, the magnitude of the potential always decreases. In common convention for such problems, assuming a positive charge, the potential decreases.