The separation between the plates of a parallel-plate capacitor is 0.500 cm and its plate area is 100 cm ^2 . A 0.400 cm thick metal plate is inserted into the gap with its faces parallel to the plates. Determine the capacitance of the assembly and whether it depends on the position of the metal plate within the gap.

Step-by-step solution

Given: Distance between plates, d = 0.500 cm = 5 10⁻³ m Area of plates, A = 100 cm ^2 = 10⁻² m ^2 Thickness of metal plate, t = 0.400 cm = 4 10⁻³ m When a metal plate of thickness t is inserted parallel to the plates of a capacitor, it acts as two capacitors in series. Let the metal plate be at a distance x from one plate. The distances of the air gaps are x and d - t - x . The equivalent capacitance C is given by: 1 C = 1 C₁ + 1 C₂ 1 C = x ₀ A + d - t - x ₀ A = d - t ₀ A C = ₀ A d - t Substituting the given values