A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates M₁ and M₂ which extend far beyond the vertical walls in all directions. The container is partitioned into two equal chambers with a thin insulating vertical wall. The partition wall contains a small hole of cross-sectional area √10 cm² near its bottom edge. Initially the hole is closed and the left chamber of the container is completely filled with a liquid of dielectric constant ε(r) = 15 and the right chamber is empty, ε(r) = 1. At time t = 0, the hole is opened and the liquid flows from the left chamber to the right chamber. In both the chambers, the space above the liquid has ε(r) = 1 and is maintained at atmospheric pressure. The schematic of the container at a time t > 0 is shown in the figure. [Given: acceleration due to gravity is 10 m s⁻².]
Physics · Capacitor · capacitor with dielectric
A container of height 2 m, length 2 m and breadth 1 m is made of insulating vertical walls and two large area horizontal metal plates M₁ and M₂ which extend far beyond the vertical walls in all directions. The container is partitioned into two equal chambers with a thin insulating vertical wall. The partition wall contains a small hole of cross-sectional area √10 cm² near its bottom edge. Initially the hole is closed and the left chamber of the container is completely filled with a liquid of dielectric constant ε(r) = 15 and the right chamber is empty, ε(r) = 1. At time t = 0, the hole is opened and the liquid flows from the left chamber to the right chamber. In both the chambers, the space above the liquid has ε(r) = 1 and is maintained at atmospheric pressure. The schematic of the container at a time t > 0 is shown in the figure. [Given: acceleration due to gravity is 10 m s⁻².]
Sub-question 1
The height (in m) of the liquid in left chamber at t = 500 s is:
Sub-question 2
The difference in the capacitance (in F) between the metal plates at t = 0 and that at t = 500 s is (8 - n)ε₀, where ε₀ is the permittivity of free space. The value of n is: