Electrostat-07-PROBLEMS

PROBLEMS 1. A small ball of mass 2 x 10-3 kg having a charge of 1 mC is suspended by a string of length 0.8 m. Another identical ball having the same charge is kept at the point of suspension. Determine the minimum horizontal velocity which should be imparted to the lower ball so that it can make complete revolution . 2. A non-conducting disc of radius a and uniform positive surface charge density s is place on the ground with its axis vertical. A particle of mass m and positive charge q is dropped, along the axis of the disc from a height H with zero initial velocity. The particle has q/m = = 4 e0g/s. (a) Find the value of H if the particle just reaches the disc. (b) Sketch the potential energy of the particle as a function of its height and find its equilibrium position. 3. A circular ring of radius R with uniform positive charge density l per unit length is located in the y-z plane with its centre at the origin O. A particle of mass m and positive charge q is projected from the point P(R 3 , 0, 0) on the positive x-axis directly towards O, with an initial speed v. Find the smallest (non-zero) value of the speed v such that the particle does not return to P. 4. A conducting sphere S1 of radius r is attached to an insulating handle. Another conducting sphere S2 of radius R is mounted on an insulating stand S2 is initially uncharged. S1 is given a charge Q brought into contact with S2 and removed. S1 is recharged such that the charge on it is again Q and it is again brought into contact with S2 and removed. This procedure is repeated n times. (a) Find the electrostatic energy of S2 after n such contacts with S1. (b) What is the limiting value of this energy as n ® ¥ ? 5. Two square metal plates of side 1 m are kept 0.01 m apart like a parallel plate capacitor in air in such a way that one of their edges is perpendicular to an oil surface in a tank filled with an insulating oil. The plates are connected to a battery of emf 500V. The plates are then lowered vertically into the oil at a speed of 0.001 ms-1. Calculate the current drawn from the battery during the process. (Dielectric constant of oil = 11, e0 = 8.85 x 10-12 C2N-1m-1). 6. Two parallel plate capacitors A and B have the same separation d = 8.85 x 10-4 m between the plates. The plate areas of A and B are 0.04 m2 and 0.02 m2 respectively. A slab of dielectric constant (relative permittivity) K = 9 has dimensions such that it can exactly fill the space between the plates of capacitors B. (i) The dielectric slab is placed inside A as shown in figure. A is then charged to a potential differ- ence of 110 V. Calculate the capacitance of A and the energy stored in it. (ii) The battery is disconnected and then the dielectric slab is removed from A. Find the work done by the external agency in removing the slab from A. (iii) The same dielectric slab is now placed inside B, filling it completely. The two capacitors a and B are then connected as shown in figure. Calculate the energy stored in the system. 7. Two isolated metallic solid spheres of radii R and 2R are charged such that both of these have the same charge density s. The spheres are located far away from each other and connected by a thin conducting wire. Find the new charge density on the bigger sphere.

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