Consider the arrangement depicted in the figure. The capacitor plates, each having a plate area A , are rigidly clamped in the laboratory. A dielectric slab of mass m is released from rest with a length a initially inside the capacitor. Disregarding any effects of friction or gravity, determine the time period of the periodic motion executed by the slab.

Step-by-step solution

Let the width of the capacitor plates be b . The area of each plate is A = bl , which gives b = A l . When a length x of the dielectric slab is inside the capacitor, the system can be considered as two capacitors in parallel: one with air and one with the dielectric. The equivalent capacitance is: C = ₀ b (l - x) d + K ₀ b x d = ₀ b d [l + (K - 1)x] The force exerted by the electric field on the dielectric slab is constant and is given by: F = 1 2 E ^2 dC dx = 1 2 E ^2 [ ₀ b (K - 1) d ] = ₀ A (K - 1) E ^2 2dl Since