Consider the situation shown in figure .The plates of the capacitor have plate area `A` and are clapmed in the laborstory . The dielectric slab is released from rest with a length a inside the capacitor. Neglecting any effect of friction or gravity, show that slab will execute periodie motion and find its time period.

Concider the situation shown in figure .The width of each plate is b.The capacitor plates are rigidly clamped in the laboratory and connected to be a battery of emf epsilon All surfaces are frictionless .Calculate the value of M for which the dielectric slab will stay in equilibrium.

Consider the situastion shown in figure. Show that if that blocks are displaced slightly in opposite directions and released, they will execute simple harmonic motion. Calculate the time period.

Consider the situation shown in figure. Initially the spring is unstretched when the system is released from rest. Assuming no friction in the puley, find the maximum eleongation of the spring.

Consider the situatioin shown in figure. The system is released from rest and the block of mass 1.0 kg is found to have a speed 0.3 m/s ater it has descended thrugh a distance of 1 m. find the coefficient of kinetic friction between the block and the table.

Figure shown pallel plate capacitors with fixed plate and connected to two batteries .The separation between the plate is the same for the two capacitors .The plates are rectangular in shape with width b and lengths l_1 and l_2. The left half of the dielectric slab has adielectric constant K_1 and the right half K_2 . neglecting any friction ,find the ratio of the emf of the right battery for which the dielctric slab may remain in equilibrium.

Find the capacitances of the capacitance shown In figure .The plate area is A and the separation between the plate is d . Different dielectric slabe in a particular part of the figure area of the same thickness and the entire gap between the plate is filled with the dielectric slabs.

A parallel plate capacitor has a plate area 3m^(2) , spaced by 3 dielectric slabs of dielectric constant 2,3,6 and of thickness 0.4mm, 0.6 mm and 1.2mm respectively. Find the effective capacity.

A rectangular plate of sides a and b is suspended from a ceiling by two parallel strings of length L each in the figure. The separation between the strings is d. The plate is displaced slightly in its plane keeping the strings tight. Show that it will execute harmonic motion. Find the time period.

Shown a parallel plate capacitor with plates of width b and length l . The separation between the platesis d. The plates are rigidly clamped and connected to a battery of emf V. A dielectric slab of thickness d and dielectric constant K is slowly inserted between the plates. (a) Calculate the energy of the system when a length x of the slab is introduced into the capacitor. (b) what force should be applied on the slab to ensure that is goes slowly into the capacitor? Neglect any effect of friction or gravity.

A capacitor is made of a flat plate of area A and B second plate having a stair -like structure as shown in figure. The width of each stair is a and the height is b . Find the capacitance of the assembly.