Electrostat-06-Subjective UnSolved

(BRUSH UP YOUR CONCEPTS) 1. The bob of a simple pendulum has a mass of 40 g and a positive charge of 4.0 x 10-6C. It makes 20 oscillations in 45 s. A vertical electric field pointing upward and of magnitude 2.5 x 104N/C is switched on. How much time will it now take to complete 20 oscillations? 2. Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming x < < R, find the time period of oscillations of the particle if it is released from there. 3. Two identically charged spheres are suspended by strings of equal length from the same point. The string makes an angle of 30° with each other, when suspended in air while in a liquid of density 0.8 gm/cc, the angle remains the same. What is the dielectric constant of the liquid? The density of the material of the sphere is 1.6 gm/cc. 4. A particle A having a charge of 1.0 × 10-6C is held fixed on a horizontal table. A second charged particle of mass 80 g stays in equilibrium on the table at a distance of 10cm from the first charge. The coefficient of friction between the table and this second particle is  = 0.1. Find the range within which the charge of this second particle may lie. 5. Find the charge appearing on each of the three capacitors shown in the figure. 6. Each capacitor shown in the figure has a capacitance of 5.0mF. The e.m.f. of the battery is 50V. How much charge will flow through AB if the switch S is closed ? S B A 7. The particle P shown in figure has a mass of 10 mg and a charge of -0.01mC. Each plate has a surface area 100 cm2 on one side. What potential difference V should be applied to the combination to hold the particle P in equilibrium ? P V 8. Figure shows two identical parallel plate capacitors connected to a battery through a switch S. Initially, the switch is closed so that the capacitors are completely charged. The switch is now opened and the free space between the plates of the capacitors is filled with a dielectric of dielectric constant 3. Find the ratio of the initial total energy stored in the capacitors to the final total energy stored. 9. A capacitor has square plated, each of side ‘a’ making an angle of  with each other as shown in figure. Calculate the capacitance of the arrangement for small  . d l 10. Fig shows two capacitor in series, the regid centre section of length ‘b’ being a b movable vertically show that equivalent capacitance of combination is independent of the position of the centre section. Also find equivalent capacetance. (CHECK YOUR SKILLS) 1. The electric field components in figure are Ex = b cube and the charge within the cube. , Ey = Ez = 0. Calculate the flux through the y x z 2. Find the magnitude of the electric field at the point P in the configuration shown in figure for d>>a. Take 2qa = p. P P P d d d -q +q -q +q +q q a a a a (a) (b) (c) 3. Two point charges + q & - q are separated by the distance 2 l. Find the flux of the electric field strength vector across a circle of radius R as shown in the figure. 4. Take the potential of the point B in figure to be zero. (a) Find the potential at the points C and D. (b) If a capacitor is connected between C and D, what charge will appear on this capacitor ? 50V 5 A spherical condenser has 10 cm & 12 cm as the radii of inner & outer spheres. The space between the two is filled with a di-electric of di-electric constant 5. Find the capacity when; (i) The outer sphere is earthed (ii) The inner sphere is earthed. 6. Each plate of a parallel plates air capacitor has an area S. What amount of work has to be performed to slowly increase the distance between the plates from x1 to x2 if : (i) The charge of the capacitor, which is equal to q, is kept constant (ii) The voltage across the capacitor, which is equal to V, is kept constant in the process. 7. A parallel plate condenser consist of two metal plates of area A & separation d. A slab of thickness t & di-electric constant K is inserted between plates with its faces parallel to the plates & having the same surface area as that of the plates with keeping constant power supply V. Find the capacitance of the system. If K = 2, for what value of t/d will the capacitance of the system be 3/2 times that of the condenser with air filling the full space ? Calculate the energy in the cases & account for the energy change. 8. The capacitance between the adjacent plates shown in figure is 50nF. A charge of 1.0mC is placed on the middle plate. (a) What will be the charge on the outer surface of the upper plate ? (b) Find the potential difference developed between the upper and the middle plates. 9. Consider the situation shown in figure. The plates of the capacitor have plate area A and are clamped in the laboratory. The dielectric slab is released from rest with length ‘a’ inside the capacitor. Ne- glecting any effect of friction or gravity, show that the slab will execute periodic motion and find its time period. l E d 10. A parallel plate capacitor with air as a dielectric is arranged horizontally. The lower plate is fixed and the other connected with a perpendicular spring. The area of each plate is A. In the steady position, the distance between the plates is d0. When the capacitor is connected with an electric source with the voltage V, a new equilibrium appears, with the distance between the plates as d1. Mass of the upper plates is m. (i) Find the spring constant K. (ii) What is the maximum voltage for a given K in which an equilibrium is possible ?