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 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.

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.

Consider4 the situation shown in figure. Bothe the pulleys and the string are light and all the surfaces are friction less. a. Find the acceleration of the mass M. b. Find the tension in the string c. Calculate the force exerted by the clamp on the pulley A in the figure.

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.

a. A closed loop is held stationary int eh magnetic field between the north and south poles of two permanent magnets held fixed. Can we hope to generate current in the loop by using very strong magnets? b. A closed loop move normal to the constant electric field between the plates of a large capacitor. Is a current induced in the loop (i) when it is wholly inside the region between the capacitor plates (ii) when it is partially outside the plates of the capacitor? The electric field is normal to the plane of the loop. c. A rectangular loop and a circular loop are moving out of a uniform magnetic field (region). (see fig.) to field-free region with a constant velocity v. In which loop do you expect the induced emf to be constant during the passage out of the field region? The field is normal to the loops. d. Predict the polarity of the capacitor in the situation described by the figure below.

Three identical lamps each having a resistance R are connected to the battery of emf as shown in the figure. Suddenly the switch S is closed. (a) Calculate the current in the circuit when S is open and closed (b) What happens to the intensities of the bulbs A,B and C. (c ) Calculate the voltage across the three bulbs when S is open and closed (d) Calculate the power delivered to the circuit when S is opened and closed (e ) Does the power delivered to the circuit decreases, increases or remain same?

Shows a situation similar to the previous problem. All parameters are the same except that a battery of emf epsilon and a variable resistance R are connected wires. Let theta be the angle made by the rod from the horizontal position (shown in the figurer), measuredin the clockwise direction. During the part of the motion Oltthetaltpi/4 the only forces acting on the rod are gravity and the forces exerted by the magnetic field and the pivot. However, during the part of the motion, the resistance R is varied in such a way that the rod continues to rotate with a constant angular velocity omega . Find the value of R in terms of the given quantities.

A parallel- plate capacitor having plate-area A and plate separation d is joined to a battery of emf epsilon and internal resistance R at t=0. Consider a plane surface of area A/2, parallel to the plates and situated symmetrically between them. Find the displacement current through this surface as a function of time.